1

Problem

The circumference of a circle is equal to its area. Find the diameter of the circle.

2

Step

Here the given data is

Circumference is equal to the area

3

Formula

Area of a circle is \$ A = πr^2\$.

4

Hint

Circumference is equal to the area = πd.

5

Step

Diameter is twice the length of the radius:

\$r = d/2\$

6

Step

Plug the value in area formula:

\$πd = π (d/2)^2\$

7

Step

After simplification:

\$πd = π(d^2)/4\$

8

Step

After simply the equation:

\$4\cancel(πd) = \cancel(πd)^2\$

\$4d = d^2\$

\$d^2 = d \times d\$

\$4\cancel(d) = \cancel(d) \times d\$

d = 4

9

Solution

Therefore, the diameter of the circle is 4 units.

9

Sumup

Please summarize steps

Choices

11

Choice-A

This option is incorrect, as it does not solve the quadratic equation.

Wrong 2 units

12

Choice-B

This option is incorrect because it is not a solution to the quadratic equation

Wrong 5 units

13

Choice-C

This option is correct and satisfies both the equation and the physical context that a circle’s diameter is d = 4

Correct 4 units

14

Choice-D

This option is incorrect as it does not provide a solution to the quadratic equation

Wrong 6 units

15

Answer

Option

C

16

Sumup

Please summarize choices