Question

An architect increases the radius of a circular window by 20 percent. By what percent did the area of the circular window increase?

Answer 1

The area of the circular window increases by 44 percent when the radius is increased by 20 percent.

Step-by-step explanation:

To find the percent increase in the area of the circular window, we first need to calculate the new area after increasing the radius by 20 percent. The formula for the area of a circle is A = πr^2. Let's assume the initial radius is r. After increasing the radius by 20 percent, the new radius becomes r + (0.2r) = 1.2r. Therefore, the new area is A' = π(1.2r)^2 = 1.44πr^2. Now, to calculate the percent increase, we can use the formula:

Percent Increase = (New Value - Initial Value) / Initial Value * 100

Substituting the values, we have:

Percent Increase = (1.44πr^2 - πr^2) / πr^2 * 100 = 0.44 * 100 = 44%