The radius of a circle is uniformly increasing at the rate of $3 c m / s$ . What is the rate of increase in area, when the radius is $10 c m$ ?

6 π

{c m}^{2} / s

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10 π

{c m}^{2} / s

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30 π

{c m}^{2} / s

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60 π

{c m}^{2} / s

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Solution

The correct option is D $60 π$ ${c m}^{2} / s$
Let $r$ be the radius of the circle and $A$ be its area.
Then, $\frac{d r}{d t} = 3 c m / s$

Now, $A = π r^{2}$
$\Rightarrow \frac{d A}{d t} = \frac{d (π r^{2})}{d t} = 2 π r \frac{d r}{d t} = 2 π (10 c m) (3 c m / s) = 60 π {c m}^{2} / s$
Option D is the correct answer.

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Q. The radius of a circle is increasing uniformly at the rate of

3 cm/s

. Find the rate at which the area of the circle is increasing when the radius is

10 cm

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The radius of a circle is uniformly increasing at the rate of 3cm/s. What is the rate of increase in area, when the radius is 10cm?

The correct option is D 60π cm2/sLet r be the radius of the circle and A be its area.Then, drdt=3cm/s Now, A=πr2 ⇒dAdt=d(πr2)dt=2πrdrdt=2π(10cm)(3cm/s)=60πcm2/sOption D is the correct answer.

The radius of a circle is uniformly increasing at the rate of $3 c m / s$ . What is the rate of increase in area, when the radius is $10 c m$ ?