Home
Class 12
MATHS
The volume of a spherical balloon is inc...

The volume of a spherical balloon is increasing at the rate of 20 `cm^3`/`sec` . Find the rate of change of its surface area at the instant when radius is 5 cm.

Text Solution

Verified by Experts

Volume of sphere is given by
`V=(4)/(3)pir^(3)`
Differentiate with respect to time
`(dV)/(dt)=(4)/(3)pi xx 3r^(2)""(dr)/(dt)`
`implies (dV)/(dt)=4pir^(3)""(dr)/(dt)`
`implies (dr)/(dt)=((dV)/(dt))/(4pir^(2))=(20)/(4pixx25)=(1)/(5pi)` cm/ second .
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise TRY YOURSELF|39 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment SECTION-A (Competition Level Questions)|50 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

The volume of a spherical balloon is increasing at a rate of 25 cm^(3)//sec . Find the rate of increase of its curved surface when the radius of balloon is 5 cm.

The surface area of spherical balloon is increasing at the rate of 2cm^(2) /sec. Find the rate of change of its volume when its radius is 5cm

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

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

The surface of a spharical balloon is increasing at a rate of 2cm^2/sec. Find the rate of increase of its volume when its radius is 6 cm.

The radius of a balloon is increasing at the rate of 10 cm/sec. At what rate is the surface area of the balloon increasing when the radius is 15 cm?

The volume of cube is increasing at a rate of 9 cm^(3)//sec . Find the rate of increase of its surface area when the side of the cube is 10 cm.

Radius of a circle is increasing at rate of 3 cm//sec Find the rate at which the area of circle is increasing at the instant when radius is 10 cm.

The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm.

The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm.