Question

What is the volume of a hollow ball whose other radius is 200m and inner radius of 100m? What is the mass if it is iron?

Answer 1

Volume of ball = Volume of outer ball - Volume of inner ball

`V = (4\pi R^3)/(3) - (4 \pi r^3)/(3)\\\\V = (4\pi)/(3)( R^3 - r^3 )\\\\V = (4\pi)/(3)( 200^3 - 100^3 )\\\\V = (4\pi)/(3)(2^3 - 1^3) * 10^6\\\\V = 2.93 * 10^7 \ m^3`

Now, density of iron is, d = 7300 kg/m³.

So, mass of iron ball is :

`m = d* V\\\\m = 7300* 2.93 * 10^7 \ kg\\\\m = 2.14 * 10^(11)\ kg`

Hence, this is the required solution.