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?
- 36 Ο cm2/sec
- 18 Ο cm2/sec
-
6 Ο cm2/sec
- 3 Ο cm2/sec
The correct answer is: C
Explanation
Increase in radius dr/dt = 0.5Area of the circular disc = Οr2
Increase in area: dA/dr = 2Οr
Rate of increase in area: dA/dt = dA/dr * dr/dt
when r = 6cm
= 2Οr * 0.5
= 2 * Ο * 6 * 0.5
2 * Ο * 6 * 1/2 = 6 Ο cm2/sec