Q6 of 168 Page 197

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

We know that circumference of a circle (C) is C = 2πr

Then, Rate of change of circumference with respect to time (t) is given by,


……………….. by chain rule


It is given that



Then,


Therefore, the rate of increase of its circumference is 1.4π cm/s.


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4

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

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A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

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The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8cm and y = 6cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.

 8

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.