Question

The area of a circle is increasing at a constant rate of 79 square centimeters per second. At the instant when the radius of the circle is 77 centimeters, what is the rate of change of the radius

Answer 1

0.51cm/s

Explanation:

Area of a circle A = πr²

r is the radius

Rate of change of area is expressed as;

dA/dt = dA/dr • dr/dt

dA/dr = 2πr

radius r = 77cm

dA/dt = 79cm²

Get dr/dt

Substitute the given values into the formula

79 = 2π(77)•dr/dt

79 = 154dr/dt

dr/dt = 79/154

dr/dt = 0.51cm/s

Hence the rate of change of the radius is 0.51cm/s