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

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 i.e. C = 2πr Different w. r. t time 𝑑𝑐﷮𝑑𝑡﷯ = 𝑑(2𝜋𝑟)﷮𝑑𝑡﷯ 𝑑𝑐﷮𝑑𝑡﷯ = 2π 𝑑𝑟﷮𝑑𝑡﷯ 𝑑𝑐﷮𝑑𝑡﷯ = 2π × 0.7 𝑑𝑐﷮𝑑𝑡﷯ = 1.4 π Since circumference is in cm & time is in sec 𝑑𝑐﷮𝑑𝑡﷯ = 1.4π 𝑐𝑚﷮𝑠𝑒𝑐﷯ 𝑑𝑐﷮𝑑𝑡﷯ = 1.4π cm/sec Hence, circumference of circle is increasing at the rate of 1.4πcm/sec