KCET · Maths · Statistics
A balloon which always remains spherical is being inflated by pumping in \( 10 \) cubic centimeters
of gas per second. Find the rate at which the radius of the balloon is increasing when the
radius is \( 15 \mathrm{cms} \).
- A \( \frac{1}{90 \pi} \mathrm{cm} s^{-1} \)
- B \( \frac{1}{9 \pi} \mathrm{cm} s^{-1} \)
- C \( \frac{1}{30 \pi} \mathrm{cm} s^{-1} \)
- D \( \frac{1}{\pi} \mathrm{cm} s^{-1} \)
Answer & Solution
Correct Answer
(A) \( \frac{1}{90 \pi} \mathrm{cm} s^{-1} \)
Step-by-step Solution
Detailed explanation
\( V = \frac{4}{3} \pi r^3 \) \( \frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt} \)
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