Question

From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid.

Answer 1

Height of the cylinder = 10 cm
Radius of the cylinder = 6 cm
The respective heights and radii of the cone and the cylinder are the same.
∴ Volume of the remaining solid = volume of the cylinder − volume of the cone
$$\begin{gathered} =\mathrm{\pi }{r}^{\mathit{2}}h\mathit{}-\frac{1}{3}\mathrm{\pi }{r}^{\mathit{2}}h\mathit{} \\ =\frac{2}{3}\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{2}{3}\times 3.14\times 6^2\times 10 \\ =753.6{\mathrm{cm}}^3 \end{gathered}$$