Q4 of 292 Page 461

The side of a square sheet of metal is increasing at 3 centimetres per minute. At what rate is the area increasing when the side is 10 cm long?

Let the side of the square be a


Rate of change of side=


Area of the square = a2


Rate of change of Area =



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2

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

 3

The radius of a circle is increasing uniformly at the rate of 0.3 centimetre per second. At what rate is the area increasing when the radius is 10 cm?

(Take π = 3.14.)


 5

The radius of a circular soap bubble is increasing at the rate of 0.2 cm/s. Find the rate of increase of its surface area when the radius is 7 cm.

 6

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?