The radius of an air bubble is increasing at the rate of 1/2 cm/s. At which rate is the volume of the bubble increasing when the radius is 1 cm?

Solution:

Derivatives are used to find the rate of changes of a quantity with respect to the other quantity. By using the application of derivatives we can find the approximate change in one quantity with respect to the

change in the other quantity.

Assuming that the air bubble is a sphere,

V = 4/3πr³

Therefore,

dV/dt = d/dt (4/3π r³) dr/dt

= 4π r² dr/dt

We have,

dr/dt = 1/2 cm/s

When r = 1 cm

Then,

dV/dt = 4π (1)² (1/2)

= 2π cm³/s

The rate at which the volume of the bubble increasing when the radius is 1 cm is 2π cm³/s

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.1 Question 12

The radius of an air bubble is increasing at the rate of 1/2 cm/s. At which rate is the volume of the bubble increasing when the radius is 1 cm?

Summary:

Given that the radius of an air bubble is increasing at the rate of 1/2 cm/s. The rate at which the volume of the bubble increasing when the radius is 1 cm is 2π cm³/s