The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At what rate is the area of the disc increasing when its radius is 6cm?
- A.
36 π cm^{2}/sec - B.
18 π cm^{2}/sec - C.
6 π cm^{2}/sec - D.
3 π cm^{2}/sec
Correct Answer: Option C
Explanation
Increase in radius dr/dt = 0.5
Area of the circular disc = πr^{2}
Increase in area: dA/dr = 2πr
Rate of increase in area: dA/dt = dA/dr * dr/dt
when r = 6cm
= 2πr * 0.5
= 2 * π * 6 * 0.5
2 * π * 6 * ^{1}/_{2} = 6 π cm^{2}/sec