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All Free Mathematics MCQs with Answers

Every Mathematics question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.

1,551 questions · page 10 of 78

181. The volume of a cube is 1728 cc. Find its surface.

  • A. 864 cm2
  • B. 648 cm2
  • C. 486 cm2
  • D. 468 cm2

Explanation: For a cube, side^3 = 1728 cm3, so the side is 12 cm because 12 x 12 x 12 = 1728 cm3.

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Correct answer: 864 cm2

182. The surface of a cube is 24sq cm. Find its volume?

  • A. 8 cc
  • B. 16 cc
  • C. 32 cc
  • D. 64 cc

Explanation: The surface area is 6a^2, so 6a^2 = 24 cm2 gives a^2 = 4 cm2 and a = 2 cm. Therefore the volume is a^3 = (2 cm)^3 = 8 cm3.

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Correct answer: 8 cc

183. The edge of a cube is 2a cm. Find its surface?

  • A. 6a2 cm2
  • B. 8a2 cm2
  • C. 12a2 cm2
  • D. 24a2 cm2

Explanation: A cube has surface area 6a^2 when its edge is a. With edge 2a cm, the surface area is 6(2a cm)^2 = 6 x 4a^2 cm2 = 24a^2 cm2.

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Correct answer: 24a2 cm2

184. A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone then the height of the cylinder is________?

  • A. 2h
  • B. 4h
  • C. 2h/3
  • D. 3h/2

Explanation: Let the common base radius be r and the cylinder height be H. The cone volume is (1/3)πr^2h, while the cylinder volume is πr^2H; since…

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Correct answer: 2h/3

185. If the radius of the sphere is doubled then it's volume is increased by?

  • A. 100 %
  • B. 200 %
  • C. 700 %
  • D. 800 %

Explanation: Sphere volume is proportional to the cube of its radius. Doubling the radius multiplies the volume by 2^3 = 8, so the increase is 8 - 1 =…

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Correct answer: 700 %

186. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

  • A. 3 : 7
  • B. 7 : 3
  • C. 6 : 7
  • D. 7 : 6Downloading Interactive Party Trivia Games

Explanation: Using curved surface area 2πrh = 264 m2 and volume πr^2h = 924 m3, division gives r/2 = 924 m3 ÷ 264 m2 = 3.5 m, so r = 7 m.

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Correct answer: 7 : 3

187. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is__________?

  • A. 90 cm
  • B. 1 dm
  • C. 1 m
  • D. 1.1 cm

Explanation: A cistern is normally understood to be open at the top. Its internal length and width are 3.3 m - 0.1 m = 3.2 m and 2.6 m - 0.1 m = 2.5 m…

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Correct answer: 1 dm

188. A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

  • A. 2 : 1
  • B. 3 : 2
  • C. 25 : 18
  • D. 27 : 20

Explanation: The total surface area of the three small cubes is 6(3 cm)^2 + 6(4 cm)^2 + 6(5 cm)^2 = 54 cm2 + 96 cm2 + 150 cm2 = 300 cm2.

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Correct answer: 25 : 18

189. Surface area of a sphere is 2464 cm2. If its radius is doubled, then the surface area of _________?the new sphere will be

  • A. 4920 cm2
  • B. 4727 cm2
  • C. 9856 cm2
  • D. 19712 cm2

Explanation: Sphere surface area is proportional to r^2. Doubling the radius makes the surface area four times as large, so the new area is 4 x 2464…

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Correct answer: 9856 cm2

190. An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.

  • A. 4 : 3
  • B. 8 : 7
  • C. 4 : 1
  • D. 6 : 5

Explanation: Let the original dimensions be 3k and 2k, so the perimeter is 10k. If the new dimensions are 7m and 3m, their perimeter is 20m, giving m =…

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Correct answer: 8 : 7

191. The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?

  • A. 91.5 cm
  • B. 93.5 cm
  • C. 94.5 cm
  • D. 92.5 cm

Explanation: The arc length is (135°/360°) x 2π x 21 cm = 15.75π cm = 49.5 cm, using π = 22/7.

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Correct answer: 91.5 cm

192. The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?

  • A. 140
  • B. 156
  • C. 175
  • D. 214

Explanation: The square's side is √1225 sq.units = 35 units, so the circle's radius is 35 units.

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Correct answer: 140

193. The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?

  • A. 81 : 121
  • B. 9 : 11
  • C. 729 : 1331
  • D. 27 : 12Everyday Science Quiz

Explanation: For cubes, volume is proportional to the cube of the side, so the side ratio is ∛(729 : 1331) = 9 : 11.

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Correct answer: 81 : 121

194. A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

  • A. 45 cm
  • B. 18 cm
  • C. 90 cm
  • D. None of these

Explanation: Equating the volumes, (4/3)π(12 cm)^3 = π(16 cm)^2L. Thus L = [4 x 12^3 cm^3]/[3 x 16^2 cm^2] = 9 cm.

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Correct answer: None of these

195. The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.

  • A. 252 m
  • B. 704 m
  • C. 352 m
  • D. 808 m

Explanation: One revolution covers the wheel's circumference: 2π x 22.4 cm = 140.8 cm, using π = 22/7.

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Correct answer: 704 m

196. The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?

  • A. Rs. 4800
  • B. Rs. 3600
  • C. Rs. 3560
  • D. Rs. 4530

Explanation: The area of the four walls is 2(25 ft + 15 ft) x 12 ft = 960 sq.ft. Openings occupy 6 ft x 3 ft = 18 sq.ft and 3 x (4 ft x 3 ft) = 36…

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Correct answer: Rs. 4530

197. A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?

  • A. 10
  • B. 100
  • C. 1000
  • D. 10000

Explanation: Each 1 m edge is 100 cm, so each edge contains 100 cm ÷ 10 cm = 10 small cubes. The total number is 10 x 10 x 10 = 1,000 cubes.

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Correct answer: 1000

198. There are two circles of different radii. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle ?

  • A. 12 π cm
  • B. 16 π cm
  • C. 24 π cm
  • D. 32 π cm

Explanation: The square has side √196 sq.cm = 14 cm, and this is half the larger circle's radius, so the larger radius is 28 cm.

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Correct answer: 24 π cm

199. A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is__________?

  • A. 3.34
  • B. 2
  • C. 4.5
  • D. 5.5

Explanation: The garden radius is 4 m ÷ 2 = 2 m, and the path increases it to 2.25 m because 25 cm = 0.25 m.

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Correct answer: 3.34

200. The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.

  • A. 4192 sq m
  • B. 4304 sq m
  • C. 4312 sq m
  • D. 4360 sq m

Explanation: Using C = 2πr, the radii are 264 m ÷ (2 x 22/7) = 42 m and 352 m ÷ (2 x 22/7) = 56 m.

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Correct answer: 4312 sq m
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