Question

The largest cone is curved out from one face of solid cube of side$21cm.$Find the volume of the remaining solid.

Answer 1

Step 1: Calculate the volume of cone

Let the maximum volume of the cone that can be carved will be of radius $=0.5$side length of cube.

Radius of cone, $R=0.5L$

$=0.5\times 21=10.5cm$

Volume of Cone;

$$\begin{gathered} V=\frac{1}{3}{\mathrm{\pi R}}^2\mathrm{h} \\ =\frac{1}{3}\mathrm{\pi }\times {\left(10.5\right)}^2\times 21 \\ =2424.52{\mathrm{cm}}^3 \end{gathered}$$

Step 2: Find the volume of wood left

The volume of wood left$=$ Volume of the cube$–V.$

The volume of wood left $={21}^3-2424.52=6836.5c{m}^3$

Hence, the volume of wood left $=6836.5c{m}^3$.