# A spherical snowball is melting in such a way that its volume is decreasing at a rate of $1 cm^{3}/min.$ The rate at which the diameter is decreasing when the diameter is $10 cms$ is

$\begin{array}{1 1}(1)\frac{-1}{50\pi}cm/min&(2)\frac{1}{50\pi}cm/min\\(3)\frac{-11}{75\pi}cm/min&(4)\frac{-2}{75\pi}cm/min\end{array}$

Let V be the volume of the spherical snow all and r be the radius at time 't'
$V= \large\frac{4}{3}$$\pi r^3 We know diameter d=2r V= \large\frac{8}{6} \pi r^3=\large\frac{\pi}{6}$$(2r)^3$
$V= \large\frac{\pi}{6}$$.d^3 \large\frac{dV}{dt} =\frac{\pi}{6}$$ \times 3d^2 \times \large\frac{d}{dt}$$(d) I=\large\frac{\pi}{2}$$ \times 10^2 \times \large\frac{d}{dt}$$(d) I=\large\frac{\pi}{2}$$ \times 10 \times 10 \times \large\frac{d}{dt}$$(d) \qquad= \large\frac{1}{50 \pi}$$cm/min$
Hence 2 is the correct answer.