Home
Class 11
PHYSICS
The volume of a sphere is given by V= ...

The volume of a sphere is given by
`V= 4/3 pi R^3`
where R is the radius of the sphere a. Find the rate of changeof volumke with respect toR. B. Find the change in volume of the sphere as the radius is increased from 20.0 cm to 20.1 cm. Assume that the rate does not appreciably change between R=20.0 cm to R=20.1 cm.

Text Solution

Verified by Experts

a. `V= 4/3 pi R^3`
or, `(dV)/(dR) = 4/3 pi d/dr (R)^3 = 4/3 pi . 3 R^3=4 pi R^2`.
b. At R=20 cm, the rate of change of volume with the radius is
`(dV)/(dR)= 4 pi R^2= (4 pi (400 cm^2)`
=1600 pi cm^2`
`= 160 pi cm^3`
Promotional Banner

Similar Questions

Explore conceptually related problems

The radius of sphere is 3.5 cm Find its surface area and volume .

Find the volume of sphere of radius 6.3 cm

Find the volume of a sphere whose radius is (i) 7 cm (ii) 0.63 cm.

The rate of cange of volume of sphere with respect to its radius r at r = 2 is __________.

Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm.

Find the rate of change of the area of a circle with respect to its radius r when (a) r=3 cm " " (b) r=4 cm

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is ……….

The volume of a sphere is 1437""1/3cm^(3) . Find its surface area.

If radius of a spherical bubble starts to increase with time t as r=0.5t . What is the rate of change of volume of the bubble with time t=4s ?