Mathematics

The radius r of a circular disc is increasing at the rate of 0.5cm/sec. At…

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 cm2/sec
  • B.
    18 π cm2/sec
  • C.
    6 π cm2/sec
  • D.
    3 π cm2/sec
Correct Answer: Option C
Explanation

Increase in radius dr/dt = 0.5
Area of the circular disc = πr2
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 cm2/sec