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

Transcript

Ex 6.1,12 The radius of an air bubble is increasing at the rate of 1 2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm? Let r be the radius of air bubble Given = 1 2 cm/s The Bubble is a sphere Volume of bubble = volume of sphere = 4 3 3 we need to find the rate at which volume of the bubble is increasing when radius is 1 cm i.e. at = 1 cm = 4 3 3 = 4 3 3 = 4 3 3 = 4 3 3 2 = 4 2 1 2 = 2 2 = 2 When radius is 1cm = 2 1 2 = 2 Since volume is in cm3 & time is in sec So = 2 cm3/sec Hence, volume is increasing at rate of 2 cm3/sec when radius = 1cm