Ex 6.1, 1 - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 6.1, 1 Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cmLet Radius of circle = 𝑟
& Area of circle = A
We need to find rate of change of Area w. r. t Radius
i.e. we need to calculate 𝒅𝑨/𝒅𝒓
We know that
Area of Circle = A = 〖𝜋𝑟〗^2
Finding 𝒅𝑨/𝒅𝒓
𝑑𝐴/𝑑𝑟 = (𝑑 (〖𝜋𝑟〗^2 ))/𝑑𝑟
𝑑𝐴/𝑑𝑟 = 𝜋 (𝑑〖(𝑟〗^2))/𝑑𝑟
𝑑𝐴/𝑑𝑟 = 𝜋(2𝑟)
𝒅𝑨/𝒅𝒓 = 𝟐𝝅𝒓
When r = 3 cm
𝑑𝐴/𝑑𝑟 = 2πr
Putting r = 3 cm
├ 𝑑𝐴/𝑑𝑟┤|_(𝑟 = 3)= 2π × 3
├ 𝑑𝐴/𝑑𝑟┤|_(𝑟 = 3) = 6π
Since Area is in cm2 & radius is in cm
𝑑𝐴/𝑑𝑟 = 6π cm2/cm
Hence, Area is increasing at the rate of 6π cm2/ cm when r = 3 cm
(ii) When r = 4 cm
𝑑𝐴/𝑑𝑟 = 2πr
Putting r = 4 cm
𝑑𝐴/𝑑𝑟 = 2π × 4
𝑑𝐴/𝑑𝑟 = 8π
Since Area is in cm2 & radius is in cm
𝒅𝑨/𝒅𝒓 = 8π cm2/cm
Hence, Area is increasing at the rate of 8π cm2/cm when r = 4 cm

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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