Question

The diameter of a certain spherical metal ball is 8.23 cm and has a mass of 2.35 kg. It has an enclosed air bubble inside whose diameter is 1.80 cm. What is the metal most likely be made out of?

Answer 1

Given,

Diameter of ball, D=8.23cm

Radius $R=\dfrac{D}{2}=\dfrac{8.23}{2}=4.115cm$

Radius of Air bubble $r=\dfrac{1.80}{2}=0.9cm$

Mass of ball $m=2.35kg=2350g$

Volume of metal, V = $\dfrac{4}{3}\pi(R^3-r^3)$

$= \dfrac{4}{3}\pi(4.115^3-0.9^3)$

$= 288.82cm^3$

We know,

$Density=\dfrac{Mass}{Volume}$

= $\dfrac{2350}{288.82} g/cm^3$

= $8.136 g/cm^3$

Hence, the metal is mostly likely to be Copper.