Question

If a metallic circular plate of radius $50\, cm$ 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 $cm^2$/hour) is

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

Answer 1

Answer: (B)

Let $A = \pi r^{2}$ be area of metalic circular plate of $r=50\,cm.$
Also, given $\frac{dr}{dt} = 1mm = \frac{1}{10}cm$
$\therefore A = \pi r^{2}$
$\Rightarrow \frac{dA}{dt} = 2\pi r\frac{dr}{dt} = 2\pi.50. \frac{1}{10} = 10\pi$
Hence, area of plate increases in $10\pi\, cm^{2}/$hour.