# Ex.11.3 Q3 Perimeter and Area - NCERT Maths Class 7

## Question

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

## Text Solution

**What is known?**

The circumference of a circular sheet is \(154\,\rm m\).

**What is unknown?**

Radius and the area of the circular sheet.

**Reasoning:**

This question is straight forward, circumference of a circular sheet is given as \(154\,\rm m\) and it will also be equal to the formula of circumference of the circle, equate them and find the value of unknown i.e. radius. Now, the radius is known put the value in the formula of area of circle and find the measurement of the area.

**Steps:**

Circumference of the circular sheet\( = 154 m\)

\[\begin{align}2\pi r &= 154\\2 \times \frac{{22}}{7} \times r &= 154\\r &= \frac{{154 \times 7}}{{2 \times 22}}\\r &= \frac{{49}}{2}\\r &= 24.5\;\rm{m}\end{align}\]

Now,

Area of circular sheet

\[\begin{align} &= \pi {r^2}\\&= \frac{{22}}{7} \times 24.5 \times 24.5\\&= 1886.5\;\rm{m^2}\end{align}\]

Thus, the radius and area of circular sheet are \(24.5 \rm \,m^2\) and \(1886.5 \rm\,m^2\) respectively.