Ex 6.1,6 - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 6.1, 6 The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference? Let r be the radius of circle
& C be the circumference of circle
Given that
Radius of a circle is increasing at the rate of 0.7 cm/sec
i.e. 𝒅𝒓/𝒅𝒕 = 0.7 cm/sec
We need find rate of change of circumference of circle w. r. 𝑡 time
i.e. we need to calculate 𝒅𝑪/𝒅𝒕
We know that
Circumference of circle = 2πr
Now,
𝑑𝐶/𝑑𝑡 = (𝑑(2𝜋𝑟))/𝑑𝑡
𝑑𝐶/𝑑𝑡 = 2π 𝒅𝒓/𝒅𝒕
𝑑𝐶/𝑑𝑡 = 2π × 0.7
𝑑𝐶/𝑑𝑡 = 1.4π
(From (1): 𝑑𝑟/𝑑𝑡 = 5 )
Since circumference is in cm & time is in sec
𝑑𝐶/𝑑𝑡 = 1.4π cm/sec
Hence, circumference of circle is increasing at the rate of 1.4π cm/sec

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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