Find the average rate of change of density with respect to the radius of a sphere in the interval [2, 5], where the density in terms of radius, r, is given by $d (r) = 3 r^{3} + 9$

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Q. Moment of inertia of a solid about its geometrical axis is given by

l = \frac{2}{5} M R^{2}

where

M

is mass &

R

is radius. Find out the rate by which its moment of inertia is changing keeping density constant at the moment

R = 1 m, M = 1 k g

& rate of change of radius w.r.t. time

2 m s^{- 1}

The average density of the earth in terms of g (acceleration due to gravity), G (Universal gravitational constant) and R (Radius of earth) is

The volume of a sphere is given by $V = \frac{4}{3} π R^{3}$
Where R is the radius of the sphere
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.