Q13 of 168 Page 197

A balloon, which always remains spherical, has a variable diameter . Find the rate of change of its volume with respect to x.

Let V be the volume of the sphere, then


It is given that, Diameter =





Now, the rate of change of its volume with respect to x is as




Therefore, the rate of change of its volume with respect to x is cm3/s.


More from this chapter

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11

A particle moves along the curve 6y = x3 +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

 12

The radius of an air bubble is increasing at the rate of . At what rate is the volume of the bubble increasing when the radius is 1 cm?

14

Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?

 15

The total cost C(x) in Rupees associated with the production of x units of an item is given by

C(x) = 0.007x3 – 0.003x2 + 15x + 4000.


Find the marginal cost when 17 units are produced.