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ID:
Class: 12
Subject: Math
Topic: Application of Derivative
Type: Short
Question:
The radius of a circle is increasing at the rate of \(0.7,\text{cm/s}\). What is the rate of increase of its circumference?
Official Solution
Explanation:
We know that \(C = 2\pi r\).
Differentiating with respect to time \(t\):
\[\frac{dC}{dt} = \frac{d}{dr}(2\pi r) \cdot \frac{dr}{dt} = 2\pi \cdot \frac{dr}{dt}\]
Given \(\frac{dr}{dt} = 0.7,\text{cm/s}\): \[\]
\(\frac{dC}{dt} = 2\pi (0.7) = 1.4\pi,\text{cm/s}\)
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