CUET · MATHS · PYQ PAPER 2025
A spherical ice ball is melting at the rate of \(100 \pi \mathrm{~cm}^3 / \mathrm{min}\). The rate at which its radius is decreasing when its radius is 15 cm, is
- A \(\frac{1}{9 \pi} \mathrm{~cm} / \mathrm{min}\)
- B \(\frac{1}{9} \mathrm{~cm} / \mathrm{min}\)
- C \(\frac{1}{18} \mathrm{~cm} / \mathrm{min}\)
- D \(\frac{1}{36} \mathrm{~cm} / \mathrm{min}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{9} \mathrm{~cm} / \mathrm{min}\)
Step-by-step Solution
Detailed explanation
\(V = \frac{4}{3} \pi r^3\) \(\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}\) \(-100 \pi = 4 \pi (15)^2 \frac{dr}{dt}\) \(-100 \pi = 900 \pi \frac{dr}{dt}\) \(\frac{dr}{dt} = -\frac{100 \pi}{900 \pi} = -\frac{1}{9} \, \mathrm{cm} / \mathrm{min}\) The rate at which its radius is…
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