# Volume of a sphere

• Jan 23rd 2010, 11:22 AM
Intrusion
Volume of a sphere
The volume of a sphere is proportional to the cube of its radius. Sphere A has volume V and radius R. The radius of Sphere B is twice the radius of Sphere A. Find the volume of Sphere B.

How would I go about doing this? Would the formula of a sphere even be needed?

Thanks for all help!
• Jan 23rd 2010, 11:28 AM
VonNemo19
Quote:

Originally Posted by Intrusion
The volume of a sphere is proportional to the cube of its radius. Sphere A has volume V and radius R. The radius of Sphere B is twice the radius of Sphere A. Find the volume of Sphere B.

How would I go about doing this? Would the formula of a sphere even be needed?

Thanks for all help!

$\displaystyle V_a=\frac{4}{3}\pi{r^3}$

$\displaystyle V_b=\frac{4}{3}\pi(2r)^3$
• Jan 23rd 2010, 11:32 AM
Intrusion
So then, the volume of sphere B will be 8V, correct? :P
• Jan 23rd 2010, 11:35 AM
You can use the sphere volume formula,

or you can simply say

$\displaystyle V_A=kR^3$

$\displaystyle V_B=k(2R)^3=k2^3R^3=8kR^3$

Whatever the volume of sphere A,
sphere B will be 8 times that.
• Jan 23rd 2010, 11:36 AM
VonNemo19
Quote:

Originally Posted by Intrusion
So then, the volume of sphere B will be 8V, correct? :P

Yes,, the volume of shpere B will be 8 times that of sphere A, or

$\displaystyle 8V_a=V_b$
• Jan 24th 2010, 05:28 AM
HallsofIvy
And notice that once you were told "The volume of a sphere is proportional to the cube of its radius" you did not need the actual formula for the volume. The radius was multiplied by 2 so the volume is multiplied by $\displaystyle 2^3= 8$.