Question

If metallic circular plate of radius $50cm$ is heated so that its radius increases at the rate of $1$ mm per hour, then the rate at which the area of the plate increases (in $c{m}^2/hr$) is.

• A. $5\pi$
• B. $10\pi$
• C. $100\pi$
• D. $50\pi$

Answer 1

The correct option is B $10\pi$

Area of the late is

$A=\pi r^2$

Differentiating with respect to $r$, we get

$\frac{dA}{dt}=2\pi r.\frac{dr}{dt}$

At $r=50cm$ we get

$\frac{dA}{dt}=2\pi .50cm.\frac{{10}^{-1}cm}{hour}$

$=100\times {10}^{-1}\pi \frac{c{m}^2}{hour}$

$=10\pi \frac{c{m}^2}{hour}$.