Question

A solid is in the form of a cone mounted on a hemisphere. The radius and height of the cone are 3 m and 4 m. Find the surface area of the given solid.

(a) 114.4 m^2

(b) 103.62 m^2

(c) 70 m^2

(d) 72.5 m^2

This question was addressed to me in exam.

Asked question is from Surface Area and Volume of Combination of Solids in portion Surface Area and Volumes of Mathematics – Class 10

Answer 1

The correct option is (b) 103.62 m^2

The explanation: Slant height = \(\sqrt {h^2 + r^2}\)

= \(\sqrt {4^2 + 3^2}\)

= √25

= 5 m

The surface area of the toy = C.S.A of the cone + C.S.A of the sphere

= πrl + 2πr^2

= (3.14 × 3 × 5) + (2 × 3.14 × 3^2)

= 47.1 + 56.52

= 103.62 m^2