Question

A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm³ /min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decrease is

• A. $\frac{1}{36\pi }$ cm/min.
• B. $\frac{1}{18\pi }$ cm/min.
• C. $\frac{1}{54\pi }$ cm/min.
• D. $\frac{5}{6\pi }$ cm/min.

Answer 1

The correct option is B $\frac{1}{18\pi }$ cm/min.

Given that
$\frac{d\vee }{dt}=50c{m}^3/min\Rightarrow \frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)=50\Rightarrow 4\pi r^2\frac{dr}{dt}=50\Rightarrow \frac{dr}{dt}=\frac{50}{4\pi (15{)}^2}=\frac{1}{18\pi }$$(herer=10+5)$