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AP EAMCET · Maths · Application of Derivatives

Air is discharging from a large spherical balloon at the rate of 4 cubic meters per minute. Then, the rate at which the surface area is shrinking when the radius of the balloon is \(8 \mathrm{~m}\), is

  1. A \(2 \mathrm{~m}^2 / \mathrm{min}\)
  2. B \(1 \mathrm{~m}^2 / \mathrm{min}\)
  3. C \(4 \mathrm{~m}^2 / \mathrm{min}\)
  4. D \(8 \mathrm{~m}^2 / \mathrm{min}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(1 \mathrm{~m}^2 / \mathrm{min}\)

Step-by-step Solution

Detailed explanation

Let air is discharging from a large spherical balloon, at the rate \(\frac{d v}{d t}=4 \mathrm{~m}^3 / \mathrm{min}\) \(\because V=\frac{4}{3} \pi r^3\), where \(r\) is the radius of spherical balloon. So,…