Ex 6.1,3 - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

Transcript

Ex 6.1, 3 The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.Let r be the radius of circle .
& A be the Area of circle.
Given that
Radius of a circle is increasing at the rate of 3 cm/s
Thus, ๐ ๐/๐ ๐ = 3 cm /sec
We need to find rate of change of area of circle w. r. t time when r = 10 cm
i.e. we need to find ๐ ๐จ/๐ ๐ when r = 10 cm
We know that
Area of circle = ฯr2
A = ฯr2
Differentiating w.r.t time
๐ ๐จ/๐ ๐ = ๐ (๐ ๐๐)/๐ ๐
๐๐ด/๐๐ก = ฯ ๐(๐2)/๐๐ก
๐๐ด/๐๐ก = ฯ ๐(๐2)/๐๐ก ร ๐ ๐/๐ ๐
๐๐ด/๐๐ก = ฯ ๐ (๐๐)/๐ ๐ ร ๐๐/๐๐ก
๐๐ด/๐๐ก = ฯ. 2r . ๐๐/๐๐ก
๐๐ด/๐๐ก = 2ฯr . ๐ ๐/๐ ๐
๐๐ด/๐๐ก = 2ฯr . 3
๐๐ด/๐๐ก = 6ฯr
When ๐ = 10 cm
โ ๐๐ด/๐๐กโค|_(๐ =10) = 6 ร ฯ ร 10
โ ๐๐ด/๐๐กโค|_(๐ =10) = 60 ฯ
(From (1): ๐๐/๐๐ก = 3)
Since area is in cm2 & time is in sec
๐๐ด/๐๐ก = 60ฯ cm2/sec
Hence, Area is increasing at the rate of 60ฯ cm2/sec when r = 10 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.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!