Ex.11.3 Q12 Perimeter and Area - NCERT Maths Class 7

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Question

The circumference of a circle is \(31.4 \rm\,cm\). Find the radius and the area of the circle? (Take \(π = 3.14\))

Text Solution

What is given ?

The circumference of a circle is \(31.4 \rm\,cm\)

What is the unknown ?

The radius and the area of the circle

Reasoning:

The circumference of the circle is given as \(31.4 \rm\,cm\), using which you can find out the radius of the circle. Now the radius is known, put it in the formula of area of circle to obtain area of the circle.

Steps:

Given,

The circumference of the circle \(=31.4\,cm\)

\[\begin{align} 2\pi r &= 31.4\\2 \times 3.14 \times r &= 31.4\\r &= \frac{{31.4}}{{6.28}}\\r &= 5\;\rm cm\end{align}\]

Then,

Area of the circle

\[\begin{align} &= \pi {r^2}\\ &= 3.14 \times 5 \times 5\\ &= 78.5\;\rm c{m^2}\end{align}\]

Therefore, the radius and the area of the circle are \(5 \rm\,cm\) and \(78.5 \rm\,cm^2\) respectively.