Question

A spherical, iron ball of radius 10 cm, coated with a layer of ice of uniform thickness, melts at the rate of $T=3mg$ . The rate at which the thickness of decreases when the thickness of ice is 5 .cm, is

• A. 1 cm/min
• B. 2 cm/min
• C. 5 cm/min
• D. 3 cm/min

Answer 1

Answer: (A)

Given, $\frac{dv}{dt}=100\pi c{m}^3/\min$ where, V is the volume of spherical ball. $\therefore$ $\frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)=100\pi$ $\Rightarrow$ $3r^2\frac{dr}{dt}=\frac{300\pi }{4\pi }$ $\Rightarrow$ ${\left[\frac{dr}{dt}\right]}_{r=5}=\frac{300}{4\times 3\times 25}=1cm/\min$