Q267 / 270 · NDA 2020 · Mathematics

The radius of a circle is increasing at the rate of $0.7 \mathrm{~cm} / \mathrm{sec}$. What is the rate of increase of its circumference?

  • Correct answer
    A
    $4.4 \mathrm{~cm} / \mathrm{sec}$
  • B
    $8.4 \mathrm{~cm} / \mathrm{sec}$
  • C
    $8.8 \mathrm{~cm} / \mathrm{sec}$
  • D
    $15.4 \mathrm{~cm} / \mathrm{sec}$

Solution

Circumference of a circle $C=2 \pi r$ Differentiating both sides w.r.t. time $(t)$. $\frac{d c}{d t}=2 \pi \cdot \frac{d r}{d t}=2 \pi \cdot(0.7)=1.4 \pi=1.4 \times \frac{22}{7}=4.4 \mathrm{~cm} / \mathrm{sec}$

Hence, the correct answer is option: 'A'.

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