Question

If the perimeter and the area of a circle are numerically equal, then the radius of
the circle is:
(1) 2 units (l) 4 units
(1) munits (iv) 7 units​

Answer 1

Answer:

1) 2 units

Step-by-step explanation:

Answer 2

Given :-

• Perimeter of the circle is equal to the area of the circle

Aim :-

• To find the radius of the circle.

Formula to use :-

Circumference/Perimeter of the circle = $2\pi r$

Area of the circle = $\pi r^{2}$

• r represents radius.

According to the question,

Circumference of the circle = Area of the circle

$2\pi r = \pi r^{2}$

By transposing $\pi r$ to the RHS (Right hand side) of the equation,

$2 = \dfrac{\pi r^{2} }{\pi r}$

$2 = \dfrac{\pi \times r \times r}{\pi \times r}$

Cancelling the common terms, we get

$2 = r$

Hence the radius of the circle will be 2 units. (option 1)

Verification :-

Let us substitute r to be 2 and verify if the area and perimeter are equal.

Area :-

$\pi r^{2}$

=> $\pi \times (2)^{2}$

=> $\pi \times 4$

=> $4\pi$

Perimeter/Circumference :-

$2\pi r$

=> $2 \times \pi \times 2$

=> $\pi \times 4$

=> $4\pi$

Therefore,

Area of the circle = Perimeter of the circle

Hence verified.

Radius = 2units (option 1)