Question

A conical hole is drilled in a circular cylinder of height $12cm$ and base radius $5cm$. The height and the base radius of the cone are the same as the Cylinder. Find the Curved Surface Area and volume of the remaining solid.

Answer 1

Given,

Height of cylindrical part $=12cm$

Height of the concical part $=12cm$

$r=5cm$ for both Cylinder and cone

The Curved Surface Area required $=$ Curved Surface area of Cylindrical $+$ Curved Surface area of Cone.

$\therefore A=2\pi rh+\pi r\left(\sqrt{h^2+r^2}\right)$ {$\because l=\sqrt{h^2+r^2}$}

$\Rightarrow A=2\pi \times 12\times 5+\pi \times 5\left(\sqrt{5^2+{12}^2}\right)$

$\Rightarrow A=581.2c{m}^2$

Now to Calculate Volume,

Volume of the solid $=$ Volume of Cylinder $-$ Volume of Cone

$\therefore Volume=\pi r^{2}h-\frac{1}{3}\pi r^{2}h$

$\Rightarrow V=\pi \times 5^2\times 12-\frac{1}{3}\pi \times 5^2\times 12$

$\Rightarrow V=628.319c{m}^3$