Question

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.

Answer 1

Let radius of the larger sphere be ‘R’

Volume of single sphere

= Vol. of sphere 1 + Vol. of sphere 2 + Vol. of sphere 3

`4/3piR^3 = 4/3pir_1^3 + 4/3pir_2^3 + 4/3pir_3^3`

`4/3piR^3 = 4/3pir6^3 + 4/3pir8^3 + 4/3pi10^3`

R³ = [6³ + 8³ + 10³]

R³ = [216 + 512 + 1000]

R³ = 1728

R³ = 12³

∴ R = 12 

Surface area of the sphere

= 4πR²

= 4 × 3.1 × 12²

= 4 × 3.1 × 12 × 12

= 1785.6 cm²