Question

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

Answer 1

Volume of the Cube $=a^3$, (Where $a=7$ cm)

$V=(7{)}^3$

$V=343c{m}^3$

Volume of conical cavity $\left(V\right)=\frac{1}{3}\pi r^{2}h$

$V=\frac{1}{3}\times 3.14\times 3^2\times 7$

$V=65.94c{m}^3$

Volume of the remaining solid $\left(V_r\right)=$Volume of the Cube-Volume of conical cavity

$V_r=343-65.94=277.60c{m}^3$