Question

A semicircular piece of paper of radius $14cm$ is rolled to form a cone of the largest possible size. Find the capacity of the cone.

• A. $721.5c{m}^3$
• B. $645.10c{m}^3$
• C. $449.64c{m}^3$
• D. $622.37c{m}^3$

Answer 1

The correct option is D $622.37c{m}^3$

Radius of semi - circular piece $=14$ cm

Circumference of semi - circle $=$ $\pi r=\frac{22}{7}\times 14$

$=44$ cm

$\therefore$ Circumference of base of cone $=44$ cm

$\Rightarrow 2\pi R=44cm\Rightarrow R=\frac{44\times 7}{2\times 22}=7cm$

Radius of semi - circular sheet = slant height of conical cup $\Rightarrow l=14cm$

Now, $R^2+h^2=l^2\Rightarrow 7^2+h^2={14}^2\Rightarrow h=\sqrt{196-49}=\sqrt{147}=7\sqrt{3}cm$

$\therefore$ Capacity of cup $=\frac{1}{3}\pi R^{2}h=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 7\sqrt{3}=622.37{cm}^3$