Numerical: mensuration MCQ — 11 Practice Questions with Answers

Explanation

Let the breadth be x m, so the length is 2x m and the height is 3 m. The area of the four walls is 2(l + b)h. Substituting gives 2(2x + x)3 = 18x. Since this equals 108, x = 6. The breadth is therefore 6 m and the length is 12 m. Volume is l x b x h = 12 x 6 x 3 = 216 m3. The other values do not satisfy both the wall-area condition and the given height.

Explanation

Each coin is treated as a small cylinder with radius 1.25 cm and height 0.2 cm, so its volume is pi x 1.25 x 1.25 x 0.2 = 0.3125 pi cubic cm. The required cylinder has radius 2.5 cm and height 10 cm, so its volume is pi x 2.5 x 2.5 x 10 = 62.5 pi cubic cm. Dividing 62.5 pi by 0.3125 pi gives 200 coins. The counts 50, 100, and 250 do not match this volume ratio.

Explanation

The inner circumference is 660 m, so the inner radius is found from 2πr = 660. Using π = 22/7, r = 660 × 7 / 44 = 105 m. The path is 14 m wide, so the outer radius is 105 + 14 = 119 m. A radius of 110 m would add only 5 m to the inner radius. A radius of 115 m would add 10 m, not 14 m. A radius of 84 m is smaller than the inner radius, so it cannot be the outer radius.

Explanation

When the sphere is melted, its volume is conserved. The sphere has radius 4 cm, so its volume is 4/3 pi x 4^3 = 256 pi/3 cubic cm. The wire is a cylinder with diameter 4 mm, that is 0.4 cm, so its radius is 0.2 cm. Its cross-sectional area is pi x 0.2^2 = 0.04 pi square cm. Length equals volume divided by area: (256 pi/3)/(0.04 pi) = 6400/3 = 2133 1/3 cm. The other lengths do not satisfy volume conservation.

Explanation

The longest straight bamboo pole that can fit inside a rectangular room is the space diagonal of the cuboid. Its length is the square root of length squared plus breadth squared plus height squared. Here it is the square root of 12 squared plus 9 squared plus 8 squared, which is the square root of 144 plus 81 plus 64, or the square root of 289. That gives 17 m. The values 19 m and 18 m exceed the space diagonal, while 15 m is only the diagonal of the floor.