Practicing Success
If the rate of change of volume of a sphere is equal to the rate of change of its radius, then its radius is equal to |
1 unit $\sqrt{2 \pi}$ units $\frac{1}{\sqrt{2 \pi}}$ unit $\frac{1}{2 \sqrt{\pi}}$ unit |
$\frac{1}{2 \sqrt{\pi}}$ unit |
Let r be the radius and V be the volume of the sphere. Then, $V =\frac{4}{3} \pi r^3$ $\Rightarrow \frac{d V}{d t} =4 \pi r^2 \frac{d r}{d t}$ $\Rightarrow \frac{d r}{d t} =4 \pi r^2 \frac{d r}{d t}$ [∵ $\frac{d V}{d t}=\frac{d r}{d t}$ (given)] $\Rightarrow 4 \pi r^2 =1 \Rightarrow r=\frac{1}{2 \sqrt{\pi}}$ |