Application of Derivatives
Rate of Change
JEE Main 2022
Grade 12
Question:
The radius of a circle is increasing at the rate of $0.7 \text{ cm/s}$. The rate of increase of its circumference is:
(1) $0.7\pi \text{ cm/s}$
(2) $1.4\pi \text{ cm/s}$
(3) $0.35\pi \text{ cm/s}$
(4) $2.8\pi \text{ cm/s}$
Step-by-Step Solution
Key Concept: Differentiate the formula $C = 2\pi r$ with respect to time $t$, then substitute the given value of $dr/dt$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)