Question

A circular metal plate is heated so that its radius increases at a rate of $0.1$ $mm/minute$. Then the rate at which the plate's area is increasing when the radius is $50$ $cm$ is

• A. $10\pi$ $m{m}^2/minute$
• B. $100\pi$ $m{m}^2/minute$
• C. $\pi$ $m{m}^2/minute$
• D. $-\pi$ $m{m}^2/minute$

Answer 1

Answer: (B)

$100\pi$ $m{m}^2/minute$

Given $r=50cm=500mm,\frac{dr}{dt}=0.1mm/minute$

Area of circle $A=\pi r^2$

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

$\frac{dA}{dt}=100\pi {mm}^2/minute$