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CUET · MATHS · PYQ PAPER 2023

The radius of a spherical ball is increasing at the rate of 1 m/sec. At the radius equal to 3m, the volume of the ball is increasing at the rate given by :

  1. A \(30\pi \text{ m}^3/\text{sec}\)
  2. B \(38\pi \text{ m}^3/\text{sec}\)
  3. C \(36 \text{ m}^3/\text{sec}\)
  4. D \(36\pi \text{ m}^3/\text{sec}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(36\pi \text{ m}^3/\text{sec}\)

Step-by-step Solution

Detailed explanation

\(V = \frac{4}{3}\pi r^3\) \(\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}\) \(\frac{dV}{dt} = 4\pi (3)^2 (1)\) \(\frac{dV}{dt} = 36\pi \text{ m}^3/\text{sec}\)