Question

Question 2
A semi-perimeter sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

Answer 1

Given, diameter of the semi - circular sheet = 28 cm
$\therefore$ Radius of the semi - circular sheet, $r=\frac{28}{2}=14cm$
The semi - circular sheet of metal is bent to form an open conical cup.
Let the radius of the conical cup be R.

$\therefore$ Circumference of base of the cone = Circumference of semi - circle
$2\pi R=\pi r$
$\Rightarrow 2\pi R=\pi \times 14\Rightarrow R=7cm$
Now,$h=\sqrt{l^2-R^2}=\sqrt{{14}^2-7^2}$
$=\sqrt{196-49}=\sqrt{147}=12.1243cm$
Volume (capacity) of conical cup $=\frac{1}{3}\pi R^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 12.1243=622.38c{m}^3$