Home
Class 12
MATHS
If volume of a sphere is changing at a r...

If volume of a sphere is changing at a rate of `20 cm^(3)//sec`, then at what rate radius will be changing 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|Exercise TRY YOURSELF|39 Videos

  • APPLICATION OF DERIVATIVES

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

  • APPLICATION OF INTEGRALS

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

Similar Questions

Explore conceptually related problems

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 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.

IF the volume of a spherical balloon is increasing at the rate of 900cm^3//sec , then the rate of change of radisu of balloon at an instant when radius is 15cm [in cm//sec ] is

If the volume of sphere changes at the rate of 140 cm^(3)//sec, then, when the radius is 70 cm, its surface area is increasing at the rate of

If the area of a circle changes at the rate of 2pi cm^(2)//sec , then, when the radius is 10cm, the radius is changing at the rate of

If the radius of a circle is increasing at a uniform rate of 2 cm/s, then find the rate of increase of area of circt the instant when the radius is 20 cm.

6) The volume of a spherical balloon is increasing at the rate of 20cm/sec. Find the rate of change of its surface area at the instant when its radius is 8cm.

The volume of a sphere is increasing at the rate of 8cm^(3)//s . Find the rate at which its surface area is increasing when the radius of the sphere is 12 cm.