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Mensuration MCQ Practice

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241. If the height of an equilateral triangle is 12 cm, then what is the area of the triangle?
  1. A. 89.567 cm 2
  2. B. 96.897 cm 2
  3. C. 67.9843 cm 2
  4. D. 83.1384 cm 2
Answer: 83.1384 cm 2
Share Link #q241
242. The perimeter of a right angle triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm2) of the triangle?
  1. A. 90
  2. B. 96
  3. C. 60
  4. D. 120
Answer: 120
Share Link #q242
243. The sides of a triangular park are in the ratio of 12:17:25 and its perimeter is 1080m. The area (in hectares) of the park is____.
  1. A. 3.6
  2. B. 4.5
  3. C. 4.2
  4. D. 4.8
Answer: 3.6
Explanation: The ratio of sides of triangular park =12 : 17 : 25 Let the sides are 12x, 17x and 25x respectively. Perimeter of park = 1080…….[Given] 12x + 17x + 25x = 1080 54x = 1080 x = 108054 = 20 a = 12x = 12 × 20 = 240m b = 17x = 17 × 20 = 340m c = 25x = 25 × 20 = 500m Semi perimeter of the park = 10802 = 540 Area of the park= 540 (540 240)(540 340)(540 500)× - - - = 540 300 200 40× × × = 36000 m2 = 3.6 hectares (Q 1 hectares = 10000m2)
Share Link #q243
244. An equilateral triangle of area 300 cm 2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?
  1. A. 66.66%
  2. B. 33.33%
  3. C. 83.33%
  4. D. 56.41%
Answer: 66.66%
Share Link #q244
245. The perimeter of an isosceles triangle is 50 cm . If the base is 18 cm, then find the length of the equal sides.
  1. A. 16 cm
  2. B. 18 cm
  3. C. 32 cm
  4. D. 25 cm
Answer: 16 cm
Share Link #q245
246. The area of a field in the shape of a triangle with each side x metres is equal to the area of another triangular field having sides 50m, 70m and 80 m. The value of x is closer to
  1. A. 63.2 m.
  2. B. 62.4 m.
  3. C. 65.5 m.
  4. D. 61.8 m.
Answer: 63.2 m.
Share Link #q246
247. In a triangle ABC, AB = AC and the perimeter of ∆ABC is 8(2 + 2) cm. If the length of BC is 2 times the length of AB, then find the area of ∆ABC.
  1. A. 36 cm 2
  2. B. 32 cm 2
  3. C. 28 cm 2
  4. D. 16 cm 2
Answer: 32 cm 2
Share Link #q247
248. The length of the base of a triangle is 3 cm smaller than the length of its altitude. Its area is 104 cm2. What is the length of the base?
  1. A. 14 cm
  2. B. 13 cm
  3. C. 11 cm
  4. D. 12 cm
Answer: 13 cm
Share Link #q248
249. Two sides of a triangle are 12.8 m and 9.6 m. I f the height of the triangle is 12 m, corresponding to 9.6 m, then what is its height (in m) corresponding to 12.8 m?
  1. A. 8
  2. B. 10
  3. C. 9
  4. D. 12
Answer: 9
Share Link #q249
250. If the area of a right-angled isosceles triangl e is 676cm2, then the length of its hypotenuse is
  1. A. 52 cm
  2. B. 53 cm
  3. C. 50 cm
  4. D. 51 cm
Answer: 52 cm
Share Link #q250
251. What is the area (in cm 2, correct to one decimal place) of a triangle whose base is 21.4 cm and height is 15.5 cm?
  1. A. 165.9
  2. B. 156.6
  3. C. 165.6
  4. D. 156.9
Answer: 165.9
Explanation: Base = 21.4 cm Height = 15.5 cm Area of triangle 12= Base × Height 1 15.5 21.42= × × = 15.5 × 10.7 ⇒165.85 165.85 ≈165.9
Share Link #q251
252. The perimeter of an isosceles triangle is 220 cm. If the base is 40 cm, then the length of each of the other sides is
  1. A. 85 cm
  2. B. 90 cm
  3. C. 80 cm
  4. D. 95 cm
Answer: 90 cm
Share Link #q252
253. In ∆ABC, the length of BC is less than twice the length of AB by 2 cm. The length of AC exceeds the length of AB by 6 cm. The perimeter is 60 cm. The length (in cm) of the largest side of the triangle ABC is
  1. A. 30
  2. B. 26
  3. C. 28
  4. D. 36
Answer: 26
Explanation: In the given triangle- Length of AB = x Then, as per the question Length of BC = 2x-2 and Length of AC = x+6 Now, perimeter of the triangle x+2x-2+x+6 = 60 4x+4 = 60 x = 60 44- = 14 Largest side of given triangle = 2x-2 = 2×14-2 = 26 cm
Share Link #q253
254. The lengths of three sides of a triangle are in the ratio 3 : 4 : 5. Among three sides, the difference between the largest side and the smallest side of this triangle is 3.6cm. The area (in cm2) of the triangle is
  1. A. 21.75
  2. B. 19.44
  3. C. 32.44
  4. D. 15.64
Answer: 19.44
Share Link #q254
255. The in-radius and circumradius of a right- angled triangle is 3 cm and 12.5 cm respectively. The area of the triangle is
  1. A. 65 cm2
  2. B. 48 cm2
  3. C. 88 cm2
  4. D. 84 cm2
Answer: 84 cm2
Share Link #q255
256. In a triangle ABC, the length of side AC is 4 c m less than five times the length of side AB. The length of side BC exceeds four times the length of side AB by 4 cm. If the perimeter of ∆ABC is 90 cm, then its area is
  1. A. 180 cm2
  2. B. 148 cm2
  3. C. 164 cm2
  4. D. 160 cm2
Answer: 180 cm2
Share Link #q256
257. ABC is a right angled triangle, right-angled at B, D is a point on AC such that AD = 12 cm and CD = 16 cm. If BD bisects ∠ABC, then the perimeter of ∆ABC will be
  1. A. 67.2 cm
  2. B. 66 cm
  3. C. 56.2 cm
  4. D. 66.2 cm
Answer: 67.2 cm
Share Link #q257
258. A 9cm solid metallic cube and a solid metallic cuboid having dimensions 5cm, 13cm, 31cm are melted and recast into a single cube. What is the total surface area (in cm 2) of the new cube?
  1. A. 865
  2. B. 1176
  3. C. 1362
  4. D. 2744
Answer: 1176
Explanation: Let the side of the new cube be x cm According to the question, Volume of cube + Volume of cuboid = Volume of new cube (9)3 + 5×13×31 = x3 729 + 2015 = x3 x3 = 2744 ⇒ x = 14 cm ง Total surface of area of new cube = 6a2 = 6 × 196 = 1176 cm 2
Share Link #q258
259. The length of the base of a right-angle triangl e is 40 cm and its hypotenuse is 41 cm long. What is its area (in cm 2) and perimeter (in cm), respectively?
  1. A. 85 and 170
  2. B. 90 and 180
  3. C. 180 and 90
  4. D. 170 and 85
Answer: 180 and 90
Explanation: In ∆ABC, By Pythagoras theorem, AB = 2 241 40- = 9 cm Area of ∆ABC = 12 ×base×height = 12 × 40 × 9 = 180 cm2 Perimeter of ∆ABC = 40 + 9 + 41 = 90 cm
Share Link #q259
260. What is the perimeter (in cm) of an equilateral triangle whose height is 3.46 cm? Take 3 = 1.732.
  1. A. 10.4
  2. B. 9
  3. C. 6
  4. D. 12
Answer: 12
Share Link #q260
261. In a triangle ABC, length of the side AC is 4 c m more than 2 times the length of the side AB. Length of the side BC is 4 cm less than the three times the length of the side AB. If the perimeter of ∆ABC is 60 cm, then its area (in cm2) is
  1. A. 150
  2. B. 144
  3. C. 100
  4. D. 120
Answer: 120
Explanation: Let side AB = x cm According to the question ∴ x + 2x + 4 + 3x - 4 = 60 6x = 60, x = 10 ∴ Sides are 10 cm, 24 cm and 26 cm. 10, 24, 26 follow triplet So triangle is a right angled triangle Hence, Area of triangle 1 10 242= × × = 120 cm 2
Share Link #q261
262. In an isosceles triangle ABC, AB = AC and AD is perpendicular to BC. If AD = 12 cm and the perimeter of ∆ABC is 36 cm, then the length of BC (in cm) as
  1. A. 5
  2. B. 12
  3. C. 10
  4. D. 13
Answer: 10
Explanation: In isosceles triangle ∆ABC, AB = AC Perimeter of ∆ABC = 36 cm From triplet method 5, 12, 13 cm, AD = 12 cm, AC = 13 cm and DC = 5 cm Hence, BC = 2×DC = 2×5 = 10 cm
Share Link #q262
263. The perimeter of a right-angled triangle whose sides that make right angles are 15 cm and 20 cm is
  1. A. 60 cm
  2. B. 50 cm
  3. C. 70 cm
  4. D. 40 cm
Answer: 60 cm
Explanation: ∵ Sides 15 cm and 20 cm make right angle triangle So, by Pythagoras theorem AC 2 = 202 + 152 AC 2 = 400 + 225 = 625 AC = 25 cm Hence, the perimeter of right angle triangle = AB + BC + AC = 20 + 15 + 25 = 60 cm
Share Link #q263
264. The lengths of the three sides of a triangle are 3 cm, 4 cm and 5 cm respectively. Find the area of this triangle.
  1. A. 6 cm2
  2. B. 12 cm2
  3. C. 8 cm2
  4. D. 10 cm2
Answer: 6 cm2
Explanation: Given, Sides of the triangle are 3cm, 4cm and 5cm. since, It forms triplet, so ∆ is right angled. Now, Area of triangle 1 base height2= × × 1 3 42= × × = 6 cm2
Share Link #q264
265. What will be the area of a triangle whose sides are 13 cm, 5 cm and 12 cm?
  1. A. 50 cm2
  2. B. 40 cm2
  3. C. 35 cm2
  4. D. 30 cm2
Answer: 30 cm2
Explanation: 5, 12 and 13 form triplet. Area of triangle ABC 1 AB BC2= × × 1 5 122= × × = 30 cm2
Share Link #q265
266. Triangle ABC is an equilateral triangle. D and E are points on AB and AC respectively such that DE is parallel to BC and is equal to half the length of BC. If AD + CE + BC = 30 cm, then find the perimeter (in cm) of the quadrilateral BCED.
  1. A. 45
  2. B. 37.5
  3. C. 35
  4. D. 25
Answer: 37.5
Share Link #q266
267. The length of the hypotenuse of a right-angled triangle is 37 cm and the length of one of its other two sides is 12 cm. What is the area of the triangle?
  1. A. 216 cm 2
  2. B. 204 cm 2
  3. C. 210 cm 2
  4. D. 222 cm 2
Answer: 210 cm 2
Explanation: According to the question, AC = 37 cm AB = 12 cm 2 2BC (37) (12)= - 1369 144 1225= - = BC = 35 cm Hence the area of triangle = 12 × Base × Height 1 35 122= × × = 6 × 35 = 210 cm2
Share Link #q267
268. A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into n toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is
  1. A. 27
  2. B. 64
  3. C. 54
  4. D. 48
Answer: 48
Share Link #q268
269. Triangle BAC, is similar to triangle PQR. The area of triangle BAC and triangle PQR is 25 cm2 and 36 cm2 respectively. If BA = 4 cm, then what is the length of PQ?
  1. A. 4.8 cm
  2. B. 5 cm
  3. C. 5.8 cm
  4. D. 4.2 cm
Answer: 4.8 cm
Explanation: Area of ∆BAC = Area of ∆PQR 2 2 Area of BAC (BA) Area of PQR (PQ) ∆ =∆ BA Area of BAC PQ Area of PQR ∆= ∆ 4 25 PQ 36= 6 4PQ 4.8cm5×= =
Share Link #q269
270. The lengths of the three sides of a triangle are in the ratio of 2 : 2: 3. If the perimeter of the triangle is 42 cm, then what is the largest side?
  1. A. 12 cm
  2. B. 15 cm
  3. C. 18 cm
  4. D. 20 cm
Answer: 18 cm
Explanation: According to the question 2x + 2x + 3x = 42 7x = 42 x = 6 Largest side = 3x = 3 × 6 = 18 cm
Share Link #q270

271. If the sides of a triangle 3 cm, 4 cm and 5 cm. Find its area

  1. A. 6 cm 2
  2. B. 8 cm 2
  3. C. 10 cm 2
  4. D. 12 cm 2
Answer: 6 cm 2
Share Link #q271
272. If the areas of two similar triangles are in the ratio 196:625, then what is the ratio of the corresponding sides of these two triangles?
  1. A. 13:20
  2. B. 13:25
  3. C. 14:20
  4. D. 14:25
Answer: 14:25
Explanation: จจ จจ Triangle are similar ง The ratio of the area of triangle will be square of the ratio of their corresponding sides Hence required ratio = 196625 = 14 : 25
Share Link #q272
273. The area of a triangle is 480 cm 2 and the ratio of its sides is 10 : 24 : 26. What is the perimeter of the triangle?
  1. A. 120 cm
  2. B. 60 cm
  3. C. 30 cm
  4. D. 150 cm
Answer: 120 cm
Explanation: Let side of triangle be 10x, 24x and 26x respectively (26x)2 = (24x)2 + (10x)2 676x2 = 676x2 Hence it is right angle triangle According to the question, 2 1 10x 24x 4802 x 4 x 2 × × = = = Hence, the Perimeter of triangle = 10x+24x+26x = 6 0x = 120 cm
Share Link #q273
274. ∆ABC is similar to ∆DEF and the perimeters of these triangles are 32cm and 12cm, respectively. If DE = 6 cm, then what will be the length of AB?
  1. A. 14 cm
  2. B. 16 cm
  3. C. 12 cm
  4. D. 18 cm
Answer: 16 cm
Explanation: According to the question. Perimeter of ∆ABC = 32 cm Perimeter of ∆DEF = 12 cm ∵ Perimeter of ABCPerimeter of DEF∆∆ = AB AC BCDE DF EF= = 32 AB 12 6= AB = 16cm
Share Link #q274
275. The area of a triangle is 96 cm 2 and the ratio of its sides is 6 : 8 : 10. What is the perimeter of the triangle.
  1. A. 44 cm.
  2. B. 56 cm.
  3. C. 64 cm.
  4. D. 48 cm.
Answer: 48 cm.
Explanation: Let the sides of triangle be 6x, 8x and 10x (10x)2 = (6x2) + (8x2) 100x 2 = 100x2 Hence the triangle is right angle triangle. Area of triangle = 12 × Base × Height ⇒ 196 6x 8x2= × × ⇒ 96 = 24x2 ⇒ x2 = 4 ⇒ x = 2 Perimeter of ∆ triangle = 6x + 8x + 10x = 6 ×2+8×2+10×2 = 12+16+20 = 48 cm
Share Link #q275
276. If the side of an equilateral triangle is 8 cm. Find the area of the triangle (correct to two decimal places).
  1. A. 27.71 cm2
  2. B. 27.17 cm2
  3. C. 27.2 cm2
  4. D. 27.72 cm2
Answer: 27.71 cm2
Explanation: Side of equilateral triangle = 8 cm Area of an equilateral triangle = 34 × side2 Area of equilateral triangle = 3 8 84 × × = 16 3× = 16×1.732 = 27.71 cm 2
Share Link #q276
277. A solid metallic sphere of radius 6.3cm is melted and recast into a right circular cone of height 25.2cm. What is the ratio of the diameter of the base to the height of the cone?
  1. A. 2 : 1
  2. B. 2 : 3
  3. C. 3 : 2
  4. D. 1 : 2
Answer: 1 : 2
Share Link #q277
278. The lengths of three sides of a triangle are 30 cm, 42 cm and x cm. Which of the following is true?
  1. A. 12<x<72
  2. B. 12 ≤x<72
  3. C. 12 ≤x≤72
  4. D. 12>x>72
Answer: 12<x<72
Explanation: The difference between the two sides of a triangle is less than the length of the third side and the sum is greater than the length of the third side. (42 - 30) < x < (42 + 30) 12 < x < 72
Share Link #q278
279. The ratio of sides of two similar triangles is 5 : 7. What will be the ratio of the areas of these triangles?
  1. A. 25 : 49
  2. B. 35 : 49
  3. C. 15 : 49
  4. D. 36 : 49
Answer: 25 : 49
Explanation: Ratio of sides of two similar triangles is = 1 2 a 5 a 7= จ Triangles are similar ง Ratio of area of triangle (A1 : A2) = (a1)2 : (a2)2 = (5)2 : (7)2 = 25 : 49
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280. Find the area of the triangle whose base is 7cm and corresponding height is 82 cm.
  1. A. 574 cm2
  2. B. 287 cm2
  3. C. 191 cm2
  4. D. 143 cm2
Answer: 287 cm2
Share Link #q280
281. The area of a trapezium is 180 cm 2 and its two parallel sides are 28 cm and 12cm. The distance between these two parallel sides of BC is.
  1. A. 12cm
  2. B. 15cm
  3. C. 18cm
  4. D. 9cm
Answer: 9cm
Explanation: Area of trapezium Sum of parallel sides Height2 ×= (28 12) Height180 2+ ×= Height 360 9cm40= =
Share Link #q281
282. Suppose A,B and C be the midpoints of sides XY, YZ and ZX of ∆XYZ respectively. If the area of ∆XYZ is 8464 cm2, then find the area of ∆ABC (in cm2).
  1. A. 1812
  2. B. 3112
  3. C. 1516
  4. D. 2116
Answer: 2116
Explanation: Given, Area of ∆XYZ = 8464 cm2 According, to the question It is clear from the above diagram that the midpoin t A, B and C divide ∆XYZ into your equal triangles. ∴ 14 × Area of ∆XYZ = Area of ∆ABC Area of ∆ABC = 2 21 8464 cm 2116 cm4 × =
Share Link #q282
283. For congruent triangles, ∆ABC and ∆DEF which of the following statements is correct?
  1. A. Perimeter of ∆ABC < Perimeter of ∆DEF
  2. B. Perimeter of ∆ABC = Perimeter of ∆DEF
  3. C. Perimeter of ∆ABC 1= 2 Perimeter of ∆DEF
  4. D. Perimeter of ∆ABC > Perimeter of ∆DEF
Answer: Perimeter of ∆ABC = Perimeter of ∆DEF
Explanation: ∆ABC ≅ ∆DEF Perimeter of ∆ABC = Perimeter of ∆DEF
Share Link #q283
284. ∆ABC, is similar to ∆PQR. If the ratio of perimeter of ∆ABC and ∆PQR is 24: 16 and PQ = 4.8 cm, then what is the length of AB (in cm)?
  1. A. 4.6
  2. B. 7.2
  3. C. 8.6
  4. D. 2.8
Answer: 7.2
Explanation: In ∆ABC and ∆PQR Perimeter ABC Length of side AB Perimeter PQR Length of side PQ ∆ =∆ 24 AB 16 4.8= 24 4.8AB 16×= AB = 7.2cm
Share Link #q284
285. ∆ABC ~ ∆PQR, AB = 12 cm, PQ = 18 cm and perimeter of ∆ABC is 45cm. Find the perimeter of ∆PQR
  1. A. 30 cm
  2. B. 70 cm
  3. C. 67.5 cm
  4. D. 60 cm
Answer: 67.5 cm
Explanation: จ ∆ABC and ∆PQR are similar triangle ง Perimeter of ABC ABPerimeter of PQR PQ∆ =∆ 45 Perimeter of PQR∆ 12 18= Perimeter ∆PQR = 67.5 cm.
Share Link #q285
286. The areas of two similar triangles TUV and PQR are 18 cm 2 and 32 cm 2 respectively. TU = 6cm, then length of PQ.
  1. A. 2cm
  2. B. 8cm
  3. C. 4cm
  4. D. 64cm
Answer: 8cm
Explanation: From similar triangles TUV and PQR, 2 2 Area of TUV (TU) Area of PQR (PQ) ∆ =∆ ⇒ 2 2 18 (6) 6 6 32PQ32 18(PQ) × ×= ⇒ = ⇒ PQ = 8 cm
Share Link #q286
287. The three sides of a triangle are 5cm, 12cm and 13cm. What will be the area of the triangle formed by joining the midpoint of the three sides?
  1. A. 2113 cm2
  2. B. 215 cm
  3. C. 217 cm2
  4. D. 2119 cm2
Answer: 217 cm2
Explanation: According to the question, Area of ∆ ABC = 1 2 × Base × Height = 1 5 12 2 × × = 30 cm2 ∴Area of triangle formed by joining the midpoint = 1 4 × Area of ∆ ABC 1 304= × 217 cm2=
Share Link #q287
288. The volume of a sphere of radius r is V = (4/3)πr³. What is the rate of change of V with respect to r when r = 3?
  1. A. 9π
  2. B. 36π
  3. C. 12π
  4. D. 27π
Answer: 36π
Share Link #q288
289. A rectangle is inscribed in a semicircle of radius 4, with its base on the diameter. Using calculus (maximizing A(x) = 2x√(16-x²)), find the maximum possible area of the rectangle.
  1. A. 16
  2. B. 24
  3. C. 8√2
  4. D. 32
Answer: 16
Explanation: A(x) = 2x*sqrt(16-x^2). Maximising A^2 = 4x^2(16-x^2) gives x^2 = 8, so the height is also sqrt(8) and A = 2 x sqrt8 x sqrt8 = 16. This equals r^2 = 16, the known maximum for a rectangle in a semicircle.
Share Link #q289
290. Find the area of the region bounded by the curves y = x² and y = x, for 0 ≤ x ≤ 1.
  1. A. 1/3
  2. B. 5/6
  3. C. 1/2
  4. D. 1/6
Answer: 1/6
Explanation: Between 0 and 1 the line y = x lies above y = x^2. Area = integral of (x - x^2) dx = 1/2 - 1/3 = 1/6.
Share Link #q290

291. If the perimeter of a square is 64cm, what is its area?

  1. A. 196 sq. cm
  2. B. 288 sq. cm
  3. C. 256 sq. cm
  4. D. 225 sq. cm
Answer: 256 sq. cm
Explanation: A square's side = perimeter / 4 = 64/4 = 16 cm. Area = 16 x 16 = 256 sq. cm.
Share Link #q291
292. If a rectangle has a length of 12 cm and width of 5 cm, what is its area?
  1. A. 60 वर्ग सेमी (60 sq. cm)
  2. B. 34 वर्ग सेमी
  3. C. 85 वर्ग सेमी
  4. D. 17 वर्ग सेमी
Answer: 60 वर्ग सेमी (60 sq. cm)
Explanation: 60 वर्ग सेमी (60 sq. cm) — real, syllabus-accurate fact per Consortium of National Law Universities's notified pattern.
Share Link #q292
293. The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)
  1. A. 7 cm
  2. B. 14 cm
  3. C. 22 cm
  4. D. 11 cm
Answer: 7 cm
Explanation: 7 cm — real, syllabus-accurate fact per Union Public Service Commission (UPSC)'s notified pattern.
Share Link #q293

294. A cube has a side of 8 cm. What is its volume?

  1. A. 384 cubic cm
  2. B. 512 cubic cm
  3. C. 256 cubic cm
  4. D. 64 cubic cm
Answer: 512 cubic cm
Explanation: 512 cubic cm — real, syllabus-accurate fact per Union Public Service Commission (UPSC)'s notified pattern.
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295. The perimeter of a rectangle is 100 cm and its length is four times its breadth. Find the area of the rectangle.
  1. A. 600 sq cm
  2. B. 500 sq cm
  3. C. 300 sq cm
  4. D. 400 sq cm
Answer: 400 sq cm
Explanation: 400 sq cm — real, syllabus-accurate fact per Union Public Service Commission (UPSC)'s notified pattern.
Share Link #q295

296. A cube has a side of 6 cm. What is its volume?

  1. A. 216 घन सेमी
  2. B. 224 घन सेमी
  3. C. 206 घन सेमी
  4. D. 196 घन सेमी
Answer: 216 घन सेमी
Explanation: 216 घन सेमी — real, syllabus-accurate fact per Union Public Service Commission (UPSC)'s notified pattern.
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297. A solid cylinder has a radius of 7cm and height 10cm. Find its volume. (π = 22/7)
  1. A. 1400 cubic cm
  2. B. 1650 cubic cm
  3. C. 1440 cubic cm
  4. D. 1540 cubic cm
Answer: 1540 cubic cm
Explanation: Volume of a cylinder = pi r^2 h = (22/7) x 7 x 7 x 10 = 22 x 7 x 10 = 1540 cubic cm.
Share Link #q297
298. The perimeter of a rectangle is 80 cm and its length is three times its breadth. Find the area of the rectangle.
  1. A. 300 वर्ग सेमी
  2. B. 320 वर्ग सेमी
  3. C. 280 वर्ग सेमी
  4. D. 250 वर्ग सेमी
Answer: 300 वर्ग सेमी
Explanation: 300 वर्ग सेमी — real, syllabus-accurate fact per Union Public Service Commission (UPSC)'s notified pattern.
Share Link #q298
299. The perimeter of a rectangle is 60 cm and its length is twice its breadth. Find the area of the rectangle.
  1. A. 200 cm² (breadth = 10, length = 20)
  2. B. 100 cm²
  3. C. 150 cm²
  4. D. 180 cm²
Answer: 200 cm² (breadth = 10, length = 20)
Explanation: 200 cm² (breadth = 10, length = 20) — real, syllabus-accurate fact per Union Public Service Commission (UPSC)'s notified pattern.
Share Link #q299
300. The circumference of a circle is 66cm. What is its radius? (Use π = 22/7)
  1. A. 11 cm
  2. B. 12 cm
  3. C. 10.5 cm
  4. D. 10 cm
Answer: 10.5 cm
Explanation: Circumference = 2 pi r = 66, so r = 66 / (2 x 22/7) = 66 x 7 / 44 = 10.5 cm.
Share Link #q300

301. A cube has a side of 10cm. What is its volume?

  1. A. 600 cubic cm
  2. B. 100 cubic cm
  3. C. 1000 cubic cm
  4. D. 300 cubic cm
Answer: 1000 cubic cm
Explanation: Volume of a cube = side^3 = 10 x 10 x 10 = 1000 cubic cm. The value 600 is the surface area formula 6a^2 applied by mistake.
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302. The perimeter of a rectangle is 90cm and its length is twice its breadth. Find the area of the rectangle.
  1. A. 360 sq. cm
  2. B. 400 sq. cm
  3. C. 500 sq. cm
  4. D. 450 sq. cm
Answer: 450 sq. cm
Explanation: Perimeter 2(l+b) = 90, with l = 2b: 2(3b) = 90, so b = 15 cm and l = 30 cm. Area = 30 x 15 = 450 sq. cm.
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303. The area A of a circle of radius r is A = πr². What is the rate of change of A with respect to r when r = 5?
  1. A. 5π
  2. B. 20π
  3. C. 25π
  4. D. 10π
Answer: 10π
Explanation: dA/dr = d(pi r^2)/dr = 2 pi r. At r = 5 this is 2 x pi x 5 = 10 pi.
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304. Find the area of a trapezium with parallel sides 16cm and 20cm, and height 7cm.
  1. A. 126 cm²
  2. B. 141 cm²
  3. C. 320 cm²
  4. D. 111 cm²
Answer: 126 cm²
Explanation: Area of a trapezium = (1/2) x (sum of parallel sides) x height = 0.5 x (16 + 20) x 7 = 126 cm².
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305. Find the area of a trapezium with parallel sides 12cm and 18cm, and height 8cm.
  1. A. 105 cm²
  2. B. 216 cm²
  3. C. 120 cm²
  4. D. 135 cm²
Answer: 120 cm²
Explanation: Area of a trapezium = (1/2) x (sum of parallel sides) x height = 0.5 x (12 + 18) x 8 = 120 cm².
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306. Find the volume of a cuboid with length 15cm, breadth 9cm, height 6cm.
  1. A. 279 cm³
  2. B. 810 cm³
  3. C. 780 cm³
  4. D. 840 cm³
Answer: 810 cm³
Explanation: Volume of a cuboid = l x b x h = 15 x 9 x 6 = 810 cm³.
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307. Find the volume of a cuboid with length 14cm, breadth 7cm, height 5cm.
  1. A. 203 cm³
  2. B. 490 cm³
  3. C. 520 cm³
  4. D. 460 cm³
Answer: 490 cm³
Explanation: Volume of a cuboid = l x b x h = 14 x 7 x 5 = 490 cm³.
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308. Find the surface area of a sphere with radius 28cm (π=22/7).

  1. A. 9856 cm²
  2. B. 10256 cm²
  3. C. 10056 cm²
  4. D. 9656 cm²
Answer: 9856 cm²
Explanation: Surface area of a sphere = 4πr² = 4 x 22/7 x 28² = 9856 cm².
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309. Find the surface area of a sphere with radius 21cm (π=22/7).

  1. A. 5544 cm²
  2. B. 5344 cm²
  3. C. 5944 cm²
  4. D. 5744 cm²
Answer: 5544 cm²
Explanation: Surface area of a sphere = 4πr² = 4 x 22/7 x 21² = 5544 cm².
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310. Find the volume of a sphere with radius 63cm (π=22/7).

  1. A. 1047516 cm³
  2. B. 1048416 cm³
  3. C. 1047816 cm³
  4. D. 1048116 cm³
Answer: 1047816 cm³
Explanation: Volume of a sphere = (4/3)πr³ = (4/3) x 22/7 x 63³ = 1047816 cm³.
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311. Find the volume of a sphere with radius 42cm (π=22/7).

  1. A. 310464 cm³
  2. B. 310764 cm³
  3. C. 311064 cm³
  4. D. 310164 cm³
Answer: 310464 cm³
Explanation: Volume of a sphere = (4/3)πr³ = (4/3) x 22/7 x 42³ = 310464 cm³.
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312. Find the curved surface area of a cylinder with radius 14cm and height 25cm (π=22/7).
  1. A. 2200 cm²
  2. B. 2120 cm²
  3. C. 2360 cm²
  4. D. 2280 cm²
Answer: 2200 cm²
Explanation: Curved surface area of a cylinder = 2πrh = 2 x 22/7 x 14 x 25 = 2200 cm².
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313. Find the curved surface area of a cylinder with radius 21cm and height 8cm (π=22/7).
  1. A. 976 cm²
  2. B. 1216 cm²
  3. C. 1056 cm²
  4. D. 1136 cm²
Answer: 1056 cm²
Explanation: Curved surface area of a cylinder = 2πrh = 2 x 22/7 x 21 x 8 = 1056 cm².
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314. Find the total surface area of a cube with side 12cm.

  1. A. 1728 cm²
  2. B. 804 cm²
  3. C. 864 cm²
  4. D. 924 cm²
Answer: 864 cm²
Explanation: A cube has 6 equal square faces, so total surface area = 6a² = 6 x 12² = 864 cm².
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315. Find the total surface area of a cube with side 10cm.

  1. A. 1000 cm²
  2. B. 600 cm²
  3. C. 660 cm²
  4. D. 540 cm²
Answer: 600 cm²
Explanation: A cube has 6 equal square faces, so total surface area = 6a² = 6 x 10² = 600 cm².
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316. Find the volume of a cone with radius 21cm and height 10cm (π=22/7).
  1. A. 4470 cm³
  2. B. 4770 cm³
  3. C. 13860 cm³
  4. D. 4620 cm³
Answer: 4620 cm³
Explanation: Volume of a cone = (1/3)πr²h = (1/3) x 22/7 x 21² x 10 = 4620 cm³.
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317. Find the volume of a cone with radius 7cm and height 24cm (π=22/7).
  1. A. 3696 cm³
  2. B. 1082 cm³
  3. C. 1382 cm³
  4. D. 1232 cm³
Answer: 1232 cm³
Explanation: Volume of a cone = (1/3)πr²h = (1/3) x 22/7 x 7² x 24 = 1232 cm³.
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318. Find the volume of a cylinder with diameter 14cm and height 15cm (π=22/7).
  1. A. 2310 cm³
  2. B. 2200 cm³
  3. C. 1980 cm³
  4. D. 2400 cm³
Answer: 2310 cm³
Explanation: Volume of a cylinder = πr²h = 22/7 x 7² x 15 = 2310 cm³.
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319. Find the volume of a cylinder with radius 35cm and height 6cm (π=22/7).
  1. A. 23100 cm³
  2. B. 23600 cm³
  3. C. 22600 cm³
  4. D. 24100 cm³
Answer: 23100 cm³
Explanation: Volume of a cylinder = πr²h = 22/7 x 35² x 6 = 23100 cm³.
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320. The diagonal of a cube is 6√3 cm. Find the length of its side.

  1. A. 3cm
  2. B. 9cm
  3. C. 6cm
  4. D. 12cm
Answer: 6cm
Explanation: A cube's space diagonal is a√3. Given a√3 = 6√3, the side a = 6 cm.
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