The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.
A) 16
B) 17
C) 16
D) 15
E) 8

Question

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.
A) 16 
B) 17 
C) 16 
D) 15 
E) 8

Quizplus · Accepted Answer

Let r be the radius of the circle. The area of the circle is πr^2 and the circumference of the circle is 2πr. The given condition can be written as:
πr^2 = 8(2πr)
πr^2 = 16πr
Dividing both sides by πr (since r cannot be 0):
r = 16
Therefore, the length of the radius of the circle is 16. Answer choice C is correct.

The Area of a Circle Is Numerically Equal to 8