Question

A metallic sphere whose radius is 4 cm is melted and cast into the shape of a right circular cone of radius 7 cm. Find the height of the cylinder?

(a) 14.48 cm

(b) 22.36 cm

(c) 16.40 cm

(d) 20.32 cm

This question was posed to me in an online interview.

This interesting question is from Conversion of Solid from One Shape to Another in division Surface Area and Volumes of Mathematics – Class 10

Answer 1

Right choice is (c) 16.40 cm

Explanation: Volume of the sphere = volume of the cone

\(\frac {4}{3}\) πr^3 = \(\frac {1}{3}\) πr^2h

\(\frac {4}{3}\) × 3.14 × 4^3 = 3.14 × 7^2 × h

h = \(\frac {4 \times 3.14 \times 3.14 \times 64}{3.14 \times 49}\)

h = 16.40 cm