AP EAMCET · Maths · Application of Derivatives
Gas is being pumed into a spherical balloon at the rate of \(30 \mathrm{ft}^3 / \mathrm{min}\). The rate at which the radius increase when it reaches the value \(15 \mathrm{ft}\), is :
- A \(\frac{1}{30 \pi} \mathrm{ft} / \mathrm{min}\)
- B \(\frac{1}{15 \pi} \mathrm{ft} / \mathrm{min}\)
- C \(\frac{1}{20} \mathrm{ft} / \mathrm{min}\)
- D \(\frac{1}{25} \mathrm{ft} / \mathrm{min}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{30 \pi} \mathrm{ft} / \mathrm{min}\)
Step-by-step Solution
Detailed explanation
Given that, \(\frac{d V}{d t}=30 \mathrm{ft}^3 / \mathrm{min}, r=15 \mathrm{ft}\) Volume of sphere, \(V=\frac{4}{3} \pi r^3\) \(\frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t} \Rightarrow 30=4 \pi(15)^2 \frac{d r}{d t}\)…
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