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8 Mar 2008 13:24:08 IST

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can any 1 tell me how to derive volume and surface area of a sphere

Engineering Entrance , JEE Main , JEE Advanced

can any 1 tell me how to derive volume and surface area of a sphere

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Sagar Saxena

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Joined: 8 Oct 2008

Posts: 8064

10 May 2012 12:51:53 IST

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Find the radius of the sphere using the known surface area, then use that value to calculate the volume.

Here is how:

surface area = 4 times pi times the radius squared.

surface area = 4(pi)r^2

90790 = 4 x 3.14 x r^2

Therefore r = The square root of (90790/(4 x 3.14)

Therefore r = 85.02

Now use this value of r to find the volume of the sphere.

volume of a sphere = 4/3 times pi times r cubed

volume = 4/3 x 3.14 x r^3

volume = 4/3 x 3.14 x (85.02)^3

Volume = 2,572,952

Second Part of Question:

Answer: Find the radius of the sphere using the known volume, then use that value to calculate the surface area.

Here's how:

volume of a sphere = 4/3 times pi times r cubed

volume = 4/3 x 3.14 x r^3

1200 = 4/3 x 3.14 x r^3

r = the cubed root of 1200/(4/3 x 3.14)

r = 17.127

Now use this value of r to find the surface area of the sphere.

surface area = 4 times pi times the radius squared.

surface area = 4(pi)r^2

surface area = 4 x 3.14 x (17.127)^2

surface area = 3684.277

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