Q. 64.5( 4 Votes )

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

Answer :

Given: Spherical balloon inflated by pumping in 900 cubic centimetres of gas per second

To find the rate at which the radius of the balloon is increasing when the radius is 15 cm

Let the radius of the given spherical balloon be r cm and let V be the volume of the spherical balloon at any instant time

Then according to the given criteria,

As the balloon is inflated by pumping 900 cubic centimetres of gas per second hence the rate of volume of the spherical balloon increases by,

We know volume of the spherical balloon is .

Applying derivative with respect to time on both sides we get,

[from equation(i)]

So when the radius is 15cm, the above equation becomes,

Hence the rate at which the radius of the balloon is increasing when the radius is 15 cm will be cm/sec.

Rate this question :

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate if its area increasing when the side of the triangle is 20 cm?

Mathematics - Board PapersFor the curve, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when

Mathematics - Board PapersThe 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 = 8 cm and y = 6 cm, find the rate of change of the area of the rectangle.

Mathematics - Board Papers