Question

From a solid cube of side $7cm$, a conical cavity of height $7cm$ and radius $3cm$ is hollowed out. Find the volume of the remaining solid.

Answer 1

Step 1: Solve for volume of cube

Given,

1. Side of cube $a=7cm$
2. Radius of cone $r=3cm$
3. Height of the cone $h=7cm$

Volume of cube$=a^3$

$$\begin{gathered} ={\left(7\right)}^3 \\ =343c{m}^3 \end{gathered}$$

Step 2: Solve for volume of cone

Volume of cone$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$$\begin{gathered} =\frac{1}{3}\times \frac{22}{7}\times {\left(3\right)}^2\times 7 \\ =66c{m}^3 \end{gathered}$$

Step 3: Solve for volume of remaining solid

Volume of remaining solid $=$Volume of cube $-$ Volume of cone

$=343-66=277c{m}^3$

Hence, volume of the remaining solid is $277c{m}^3$