Volume of a sphere

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January 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!
January 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!

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

$V_b=\frac{4}{3}\pi(2r)^3$
January 23rd 2010, 11:32 AM
Intrusion

So then, the volume of sphere B will be 8V, correct? :P
January 23rd 2010, 11:35 AM
Archie Meade

You can use the sphere volume formula,

or you can simply say

$V_A=kR^3$

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

Whatever the volume of sphere A,
sphere B will be 8 times that.
January 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

$8V_a=V_b$
January 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 $2^3= 8$ .

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