If the circumference of a circular sheet is $154\ m$, find its radius. Also find the area of the sheet. $(Take\ \pi=\frac{22}{7})$

Given:

The circumference of a circular sheet is \( 154 \mathrm{~m} \).

To do:

We have to find the radius and area of the sheet.

Solution:

Let the radius of the sheet be $r$.

This implies,

$2 \pi r=154\ m$

$2\times\frac{22}{7}\times r=154$

$r=\frac{7\times7}{2}$

$r=\frac{49}{2}\ m$

Area of the sheet$= \pi r^2$

$=\frac{22}{7}\times\frac{49}{2}\times\frac{49}{2}$

$=\frac{11\times7\times49}{2}$

$=\frac{3773}{2}$

$=1886.5\ m^2$

The radius of the sheet is $24.5\ m$ and the area of the sheet is $1886.5\ m^2$.