#### Question

The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increase of its area when the radius is 12 cm, is

144 π cm

^{2}/sec2.4 π cm

^{2}/sec0.24 π cm

^{2}/sec0.024 π cm

^{2}/sec

#### Solution

0.24 π cm^{2}/sec

\[\text { Let r be the radius and A be the area of the circular plate at any timet.Then,} \]

\[A=\pi r^2 \]

\[\Rightarrow\frac{dA}{dt}=2\pi r\frac{dr}{dt}\]

\[\Rightarrow\frac{dA}{dt}=2\pi\left( 12 \right)\left( 0 . 01 \right)\]

\[\Rightarrow\frac{dA}{dt} {=0.24\pi \ cm}^2 /sec\]

Is there an error in this question or solution?

Solution The Radius of a Circular Plate is Increasing at the Rate of 0.01 Cm/Sec. the Rate of Increase of Its Area When the Radius is 12 Cm, is (A) 144 π Cm2/Sec Concept: Rate of Change of Bodies Or Quantities.