Ex.12.1 Q5 Areas Related to Circles Solution - NCERT Maths Class 10

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Question

Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(A) \(2\) units

(B) \(\pi \) units

(C) \(4\) units

(D) \(7\) units

Text Solution

What is known?

Perimeter and area of the circle are numerically equal.

What is unknown?

Radius of circle.

Reasoning:

Given that Perimeter and area of the circle are numerically equal. We get \(2\pi \rm{r}= \pi \rm{r^2}.\)

Using this relation we find the radius.

Steps:

Let the radius of the circle \(= r.\)

Circumference of circle \( = 2\pi r\)

Area of circle \(= \pi \rm{r^2}\)

Given that, the circumference of the circle and the area of the circle are equal.

This implies \[\begin{align}2\pi \rm{r} &= \pi \rm{r^2}\\2 &= \rm{r}\end{align}\]

Therefore, the radius of the circle is \(2\) units.

Hence, the correct answer is \(\rm{A.}\)

  
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