volume of sphere

Question

Show that where the radius of a circle of  a sphere is doubled, its volume of the sphere increases by 8 times.

Answer 1

The volume of a sphere is V = (4/3)πr³

 

So, if the radius is doubled, then the volume of that sphere is         

    (4/3)π(2r)³ = (4/3)π(8r³)

 

                      = 8[(4/3)πr³] = 8V

Answer 2

Hi Sandy, the equation for the volume of a sphere is given by: V = 4/3 * pi * r³.

 

All numbers are rounded.

 

Let r = 1, then the volume of the sphere is: V = 4/3 * pi * 1 = 4/3 * pi ≈ 4.189

 

Double r to 2 gives: V = 4/3 * pi * 8 = 32/3 * pi ≈ 33.510

 

Double r to 4 gives: V = 4/3 * pi * 64 = 256/3 * pi ≈ 268.082

 

Dividing 33.510 / 4.189 ≈ 8.0, or volume with radius of 2 is 8 times the volume with radius of 1.

 

Dividing 268.082 / 33.510 ≈ 8.0, or volume with radius of 4 is 8 times the volume with radius of 2.

 

Questions?

 

 

Answer 3

Formula for the volume of a sphere is

 

V  =  4/3 pi x r³  Now if you double r and make it 2r

 

Then (2r)³  becomes 8r³and the volume increases 8 times.  Not too bad

Answer 4

Volume of a sphere is V =4πr³/3

If I double the radius r' = 2r

then the new volume V' = 4πr'³/3 = 4π(2r)³/3 = 32πr³/3 = 8V