Question

Find the surface area of the given solid which is in the form of a cone mounted on a hemisphere. The radius and height of the cone are 5cm and 12cm.

(a) 214.4 cm^2

(b) 279.53 cm^2

(c) 70 cm^2

(d) 72.5 cm^2

The question was asked in an online interview.

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

Answer 1

The correct answer is (b) 279.53 cm^2

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

= \(\sqrt {12^2+5^2}\)

= √169

= 13cm

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

= πrl + 2πr^2

= (3.14 × 3 × 13) + (2 × 3.14 × 5^2)

= 47.1 + 56.52

= 279.53cm^2