Question

Given that a circle has a radius of 4inches and then a radius of 12inches after it has expanded. Given that the formula for a circle is ()=2, what is the rate of change?

Answer 1

Rate of change = 3π or 9.43

Step-by-step explanation:

Given the following data;

Initial radius, R1 = 4 inches

Final radius, R2 = 12 inches

To find the rate of change;

First of all, we would determine the area of the circle.

Mathematically, the area of a circle is given by the formula;

Area of circle = πr²

For initial radius, R1;

Area of circle, A1 = πR1²

Area of circle, A1 = 4π square inches

For final radius, R2;

Area of circle, A2 = πR2²

Area of circle, A2 = 12π square inches

Now, we can find the rate of change;

Rate of change = A2/A1

Rate of change = 12π/4π

Rate of change = 3π (in terms of pie).