Question

The length of a circle's radius is decreased by 15%.



What is the resulting percent decrease in the circle's area?

Answer options with 4 options
A.
2.3%

B.
15.0%

C.
22.5%

D.
27.75%

Answer 1

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.

If the radius is decreased by 15%, then the new radius would be 85% of the original radius.

Let's calculate the resulting percent decrease in the area:

Original radius = r
New radius = 0.85r

Original area = πr^2
New area = π(0.85r)^2 = 0.7225πr^2

Percent decrease in area = ((Original area - New area) / Original area) * 100
Percent decrease in area = ((πr^2 - 0.7225πr^2) / πr^2) * 100
Percent decrease in area = (0.2775πr^2 / πr^2) * 100
Percent decrease in area = 27.75%

Therefore, the resulting percent decrease in the circle's area would be 27.75%.

D. 27.75%