What happens to the volume of a sphere when the radius is doubled?
2007-03-29 12:53:20 · 4 answers · asked by Lx 1 in Science & Mathematics ➔ Mathematics
n=pi a=larger sphere
R=radius b=smaller sphere
{4/3nR(a)^3} - {4/3nR(b)^3} = R(a) - R(b)
If you subtract the radius of the larger (doubled) sphere
from the smaller one, you should see the difference!
2007-03-29 13:10:08 · answer #1 · answered by Ammy 6 · 0⤊ 0⤋
Notice the formula for the volume of a sphere:
V = 4/3 * pi * r^3.
Since, we are only concerned about the radius, let's only look at the radius.
r^3
When you double the original radius, what happens?
(2r)^3
8r^3
Notice how the the r^3 is now multiplied by 8, and so the volume is multiplied by 8.
2007-03-29 19:58:22 · answer #2 · answered by Sunny C 1 · 0⤊ 0⤋
Since the volume is proportional to the radius^3, doubling the radius means an eight-fold volume increase.
2007-03-29 20:00:17 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋
it goes up by a factor of 8
( v = 4/3 pi r^3 )
2007-03-29 19:57:16 · answer #4 · answered by hustolemyname 6 · 1⤊ 0⤋