Gas is being pumed into a spherical balloon at the rate of $30 \mathrm{ft}^3 / \mathrm{min}$. The rate at which the radius increase when it reaches the value $15 \mathrm{ft}$, is :

Question

Aicharya · Accepted Answer

Given that, $\frac{d V}{d t}=30 \mathrm{ft}^3 / \mathrm{min}, r=15 \mathrm{ft}$ Volume of sphere, $V=\frac{4}{3} \pi r^3$ $\frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t} \Rightarrow 30=4 \pi(15)^2 \frac{d r}{d t}$ $	herefore \quad \frac{d r}{d t}=\frac{1}{30 \pi} \mathrm{ft} / \mathrm{min}$

Gas is being pumed into a spherical balloon at the rate of $30 \mathrm{ft}^3 / \mathrm{min}$. The rate at…

Solution