The radius of an air bubble is increasing at the rate of 0.5 centimetr

1.	The radius of an air bubble is increasing at the rate of 0.5 centimetre per second. At what rate is the volume of the bubble increasing when the radius is 1 centimetre?
Answer» We know that a soap bubble will be in sphere shape Consider the radius of soap bubble as r dr/dt = 0.5 cm/s The volume of soap bubble = 4/3 πr³ Here the rate of change of volume = 4 πr² dr/dt By substituting the values = 4 × 3.14 × 1² × 0.5 We get dV/dt = 6.28 cm³/s

The radius of an air bubble is increasing at the rate of 0.5 centimetre per second. At what rate is the volume of the bubble increasing when the radius is 1 centimetre?

Answer»

We know that a soap bubble will be in sphere shape

Consider the radius of soap bubble as r

dr/dt = 0.5 cm/s

The volume of soap bubble = 4/3 πr³

Here the rate of change of volume = 4 πr² dr/dt

By substituting the values

= 4 × 3.14 × 1² × 0.5

We get

dV/dt = 6.28 cm³/s