A balloon which always remains spherical is being inflated by pumping in 900 cubic cm of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{\pi} \) cm/s
Let r be the radius and V the volume of the balloon at time t.
\( \displaystyle V=\frac{4}{3}\pi r^{3} \)
Differentiating with respect to t (rate of change),
\( \displaystyle \frac{dV}{dt}=4\pi r^{2}\frac{dr}{dt} \)
With \( \frac{dV}{dt}=900 \) and r = 15,
\( \displaystyle 900=4\pi(15)^{2}\frac{dr}{dt} \)
\( \displaystyle \frac{dr}{dt}=\frac{900}{900\pi} \)
\( \displaystyle =\frac{1}{\pi}\ \text{cm/s} \)
NCERT (2026-27 edition):
Rate of Change of Quantities
