The radius of a circle is increasing at the rate of 0.7 cm / . What is the rate of increase of its circumference?

Correct answer: A. 4.4 cm / Circumference of a circle C=2 π r Differentiating both sides w.r.t. time (t) . (d c)/(d t)=2 π · (d r)/(d t)=2 π ·(0.7)=1.4 π=1.4 × (22)/(7)=4.4 cm /

NDA 2020

Exam: NDA
Year: 2020
Subject: Mathematics
Chapter: Application of Derivatives

NDA 2020 · Mathematics · Application of Derivatives

The radius of a circle is increasing at the rate of 0.7 cm / . What...

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?

Options

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

Correct answer

A. $4.4 \mathrm{ cm} / \mathrm\sec$

Step-by-step 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

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