MHT CET · Maths · Application of Derivatives
The radius of the base of a cone is increasing at the rate \(3 \mathrm{~cm} /\) minute and the altitude is decreasing at the rate \(4 \mathrm{~cm} /\) minute. The rate at which the lateral surface area is changing, when the radius is 7 cm and altitude is 24 cm . is
- A \(75 \pi \mathrm{~cm}^2 /\) minute
- B \(25 \pi \mathrm{~cm}^2 /\) minute
- C \(3 \pi \mathrm{~cm}^2 /\) minute
- D \(54 \pi \mathrm{~cm}^2 /\) minute
Answer & Solution
Correct Answer
(D) \(54 \pi \mathrm{~cm}^2 /\) minute
Step-by-step Solution
Detailed explanation
\( l = \sqrt{r^2 + h^2} \) \( l = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25 \mathrm{~cm} \)
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