Question

Three metallic spheres of radius 2 cm, 4 cm, 8 cm are melted into a single sphere. Find the radius of the resulting sphere.

(a) 1009.4 cm^3

(b) 2446.25 cm^3

(c) 1520 cm^3

(d) 2869.4 cm^3

I got this question during a job interview.

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

Answer 1

Right answer is (b) 2446.25 cm^3

Explanation: Volume of the resulting sphere = sum of the volumes of all three spheres

= \(\frac {4}{3}\)π2^3 + \(\frac {4}{3}\)π4^3 + \(\frac {4}{3}\)π8^3

= \(\frac {4}{3}\) × 3.14(2^3 + 4^3 + 8^3)

= 2446.25 cm^3