Question

A piece of copper having an internal cavity weighs $264\mathrm{g}$ in air and $221\mathrm{g}$ in water, Find the volume of the cavity. (Take the density of copper as $8.8\mathrm{g}/\mathrm{cc}$).

Answer 1

Step 1: Given data

Density of copper $=8.8\mathrm{g}/\mathrm{cc}$

Weight in air $=264\mathrm{g}$

Weight in water $=221\mathrm{g}$

We have to find the volume of the cavity.

Step 2: Finding the volume of copper block and the total volume of copper block + cavity

Mass of copper in air $=264\mathrm{gm}$

Mass of copper in water $=221\mathrm{gm}$

Apparent loss of mass in water $=264–221=43\mathrm{gm}$

Mass of water displaced by copper piece when completely immersed in water$=43\mathrm{gm}$

Volume of water displaced $=\frac{\mathrm{mass}\mathrm{of}\mathrm{water}\mathrm{displaced}}{\mathrm{density}\mathrm{of}\mathrm{water}}=\frac{43}{1}=43\mathrm{cc}$

We know,

the volume of water displaced = the volume of copper immersed

Therefore, the volume of the copper piece including the volume of the cavity$=43cc$

Volume of copper block excluding the cavity $=\frac{\mathrm{mass}\mathrm{of}\mathrm{copper}}{\mathrm{density}}=\frac{264}{8.8}=30\mathrm{cc}$

Step 3: Find the volume of the cavity.

The volume of the piece of copper including the cavity is equal to the volume of water.

Therefore,

Volume of cavity $={\mathrm{V}}_{\mathrm{water}}-{\mathrm{V}}_{\mathrm{copper}}$

$=43-30$

$=13$

Hence, the volume of the cavity is $13\mathrm{cc}$.