SOLUTION: A sphere with center A has a surface area of 144 pi units squared. Find the volume of a sphere with center B whose radius is twice as large as the sphere with center A. What is the
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Question 284386: A sphere with center A has a surface area of 144 pi units squared. Find the volume of a sphere with center B whose radius is twice as large as the sphere with center A. What is the ratio of the volumes of the two spheres?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The surface area of a sphere is given by:
So if the surface area of your sphere is 
square units, then the radius must be 6 units. (Verification left as an exercise for the student).
The volume of a sphere is given by:
Twice the radius of Sphere A is 12, so just substitute 12 into the Volume formula and do the arithmetic.
If you have two spheres, one of radius 
and the other of radius 
then their volumes are in the ratio of:
^3}{\frac{4}{3}\pi \left(r_1\right)^3}\ =\ \frac{\left(r_2\right)^3}{\left(r_1\right)^3}\ =\ \left(\frac{r_2}{r_1}\right)^3)
Substitute and do the arithmetic.
John
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