Question

The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

विकल्प

• 6 πr

• 60 πcm²/sec

• 6 πcm²/sec

• 60 π

Answer 1

60 πcm²/sec

Explanation:

Let `r` be the radius of the circle

∴ Rate of increasing of radiu = `(dr)/(dt)` = 30 cm/sec

Area of circle = `pir^2` = A  .....(Say)

∴ `(dA)/(dt) = d/(dt) (pir^2) = d/(dt) (pir^2) * (dr)/(dt) = 2pir xx 3 = 6pir`

Where, r = 10,

The rate of change of area = `6pi xx 10` = 60 πcm²/sec.