Question

A largest possible right-circular cylinder is cut from a wooden cube of edge 7 cm. The volume of the wood left over after cutting the cylinder is __________.

Answer 1

The largest possible right circular cylinder that can be cut off from a wooden cube of given edge is such that the diameter of the cylinder is same as the edge of the cube and height of the cylinder is same as the edge of the cube.

Let r be the radius and h be the height of the largest right circular cylinder cut from a wooden cube of edge 7 cm.

∴ Diameter of the cylinder = Edge of the cube = 7 cm

⇒ 2r = 7 cm

⇒ r = $\frac{7}{2}$ cm

Height of the cylinder = Edge of the cube = 7 cm

∴ h = 7 cm

Now,

Volume of the wood left over after cutting the cylinder

= Volume of the cube − Volume of the cylinder

= (Edge)³ − $\mathrm{\pi }$r²h

$={\left(7\mathrm{cm}\right)}^3-\frac{22}{7}\times {\left(\frac{7}{2}\mathrm{cm}\right)}^2\times 7\mathrm{cm}$

= 343 cm³ − 269.5 cm³

= 73.5 cm³

Thus, the volume of the wood left over after cutting the cylinder is 73.5 cm³.

A largest possible right-circular cylinder is cut from a wooden cube of edge 7 cm. The volume of the wood left over after cutting the cylinder is ___73.5 cm³___.