Question

A toy is in the form of a cone mounted on a hemisphere and a cylinder. The radius and height of the cone are 3 m and 4 m. Find the volume of the given solid?

(a) 193.21 m^3

(b) 207.30 m^3

(c) 184.21 m^3

(d) 282.21 m^3

The question was asked at a job interview.

Question is taken from Surface Area and Volume of Combination of Solids topic in portion Surface Area and Volumes of Mathematics – Class 10

Answer 1

The correct choice is (b) 207.30 m^3

Explanation: Volume of the toy = volume of the cone + volume of the hemisphere + volume of the cylinder

= \(\frac {1}{3}\)πr^2h + \(\frac {2}{3}\)πr^3 + πr^2h

= (\(\frac {1}{3}\) × 3.14 × 3^2 × 4) + (\(\frac {2}{3}\) × 3.14 × 3^3) + (3.14 × 3^2 × 4)

= 207.30 m^3