If the radius of a circle be increasing at a uniform rate of 2cm/s. The rate of increasing of area of circle, at the instant when the radius is 20cm, is

Question

If the radius of a circle be increasing at a uniform rate of $2 \mathrm{~cm} / \mathrm{s}$. The rate of increasing of area of circle, at the instant when the radius is $20 \mathrm{~cm}$, is

(a) $70 \pi \mathrm{cm}^2 / \mathrm{s}$

(b) $70 \mathrm{~cm}^2 / \mathrm{s}$

(c) $80 \pi \mathrm{cm}^2 / \mathrm{s}$

(d) $80 \mathrm{~cm}^2 / \mathrm{s}$

Answer 1

SOLUTION — Given $\frac{d r}{d t}=2 \mathrm{~cm} / \mathrm{s}$, where $r$ be radius of circle and $t$ be the time.

Now, area of circle is given by $A=\pi r^2$

$\begin{array}{l}\frac{d A}{d t}=2 \pi r \frac{d r}{d t} \Rightarrow \frac{d A}{d t}=2 \pi \cdot 20 \cdot 2 \\\Rightarrow \quad \frac{d A}{d t}=80 \pi \mathrm{cm}^2 / \mathrm{s} \\\end{array}$

So, The correct option of this question will be (C).