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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 \( 15 \mathrm{cms} \).

  1. A \( \frac{1}{90 \pi} \mathrm{cm} s^{-1} \)
  2. B \( \frac{1}{9 \pi} \mathrm{cm} s^{-1} \)
  3. C \( \frac{1}{30 \pi} \mathrm{cm} s^{-1} \)
  4. D \( \frac{1}{\pi} \mathrm{cm} s^{-1} \)
Verified Solution

Answer & Solution

Correct Answer

(A) \( \frac{1}{90 \pi} \mathrm{cm} s^{-1} \)

Step-by-step Solution

Detailed explanation

\( V = \frac{4}{3} \pi r^3 \) \( \frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt} \)