Question

Find the volume of metal used to construct a hollow metallic sphere of internal and external diameters as $10$ cm and $13$ cm respectively.

Answer 1

Dimensions of the hollow metallic sphere are,

Internal diameter $\left(d\right)=10$ m.

Internal radius $\left(r\right)=\frac{d}{2}=102=5$ cm.

External diameter $\left(D\right)=13$ cm.

External radius $\left(R\right)=\frac{D}{2}=\frac{13}{2}=6.5$ cm

Volume of the hollow metallic sphere

$=\frac{4}{3}\times \pi (R^3-r^3)$

$=\frac{4}{3}\times 3.14\times \left(\right(6.5{)}^3-\left(5{)}^3\right)$

$=\frac{4}{3}\times 3.14\times [274.625-125]$

$=4.187\times 149.625$

$=626.43c{m}^3$