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?

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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