Question

The mass of solid sphere of metal 5 cm in diameter is 6.25 kg. Find the mass of spherical shell of the same metal, the external diameter being 10cm and thickness 1cm.

Answer 1

volume of the 5/2 cm sphere
= (4/3)π(5/2^3) = (625/6)π cm^3

volume of shell
= (4/3)π(5^3) - (4/3)π(4^3)
= (244/3)π cm^3

since the mass is a function of the volume,

(625/6)π × X = (244/3)π × 6.25
X = 48.8kg

Answer 2

The mass of a metal sphere with an external diameter of 10 cm and a thickness of 1 cm is 235.2 kg.

Given that,

A solid metal spherical of 5 cm in diameter weighs 6.25 kilogram.

We have to find the mass of a metal sphere with an external diameter of 10 cm and a thickness of 1 cm.

We know that,

m is sphere =6.25 kg

Volume of sphere =  $\frac{4}{3}$πr³

=  $\frac{4}{3}$×π×(2.5)³

= $\frac{62.5\pi}{3}$

Density of metal = $\frac{m}{v}$= $\frac{6.25}{\frac{62.5\pi}{3} }$ = $\frac{3}{10}$π kg/m³

Volume of shell =  $\frac{4}{3}$π(R³ - r³)

= $\frac{4}{3}$π(10³ - 8³)

= 784π

Mass of shell = d×v =  $\frac{3}{10}$π × 784π = 235.2 kg

Therefore, The mass of a metal sphere with an external diameter of 10 cm and a thickness of 1 cm is 235.2 kg.

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