Question

the volume of a sphere is given by V=4/3 pi r^3 where r is a radius of sphere. The changes in volume of the sphere in(cm^3) as its radius increases from 20 cm to 20.1 is..
Ans. 160pi
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Answer 1

Explanation:

let radius of first sphere =r

radius of second sphere=R

difference between volume of spheres

=4/3πR^3 - 4/3πr^3

by taking 4/3π common

=4/3π(R^3-r^3)

=4/3π[ (20.1)^3 - (20)^3 ]

=4/3π (120)

=160π

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Answer 2

The change in volume of the sphere is $160\pi$.

Explanation:

The volume of a sphere is given by :

$V=\dfrac{4}{3}\pi r^3$

If r = 20 cm, volume becomes :

$V=\dfrac{4}{3}\pi (20)^3$

If r = 20.1 cm, volume becomes :

$V=\dfrac{4}{3}\pi (20.1)^3$

Change in volume becomes :

$\Delta V=\dfrac{4}{3}\pi (20.1^3-20^3)\\\\\Delta V=160.8\pi$

So, the change in volume of the sphere is $160\pi$.

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