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 :
- A \(30\pi \text{ m}^3/\text{sec}\)
- B \(38\pi \text{ m}^3/\text{sec}\)
- C \(36 \text{ m}^3/\text{sec}\)
- D \(36\pi \text{ m}^3/\text{sec}\)
Answer & Solution
Correct Answer
(D) \(36\pi \text{ m}^3/\text{sec}\)
Step-by-step Solution
Detailed explanation
\(V = \frac{4}{3}\pi r^3\) \(\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}\) \(\frac{dV}{dt} = 4\pi (3)^2 (1)\) \(\frac{dV}{dt} = 36\pi \text{ m}^3/\text{sec}\)
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