The radius of a circle is decreasing at a constant rate of 0.1 centimeters per second. In terms of the circumference C, what is the rate of the area of the circle, in square centimeters per second?

Question

a. -(0.2)pie C
b. -(0.1)C
c. -(0.1)C/2 pie
d. (0.1)^2C
e. (0.1)^2 pie C

Answer 1

C=2πr

A=πr²
dA/dr=2πr=C

dr/dt=-0.1 cm/sec

dA/dt
= dA/dr * dr/dt
= 2πr (-0.1) cm²/s
= -0.1C cm²/s