Question

What happens to the area of a circle if the circumference is doubled?

A. The area is 1/2 of the original circle
B. The area is the same as the original circle
C. The area is 2 times the original circle
D. The area is 4 times the original circle
E. The area is 8 times the original circle

Answer 1

Solution given:

area of a circle[A]=πr²

circumference of circle [C]=2πr

when circumference of circle is doubled

it becomes :4πr

Explanation:

area directly proportional to circumference

πr²=2πr

when circumference is doubled

πr²=2(2πr)

so area

C. The area is 2 times the original circle

Answer 2

• D. The area is 4 times the original circle

Explanation:

The circumference:

• C = 2πr

If the circumference is doubled, it means the radius is doubled.

The area:

• A = πr²

And the new area:

• A1 = π(2r)² = 4πr² = 4A

Correct choice is D