Question 284386
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The surface area of a sphere is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ SA_{sph}\ =\ 4\pi r^2]


So if the surface area of your sphere is *[tex \Large 144\pi] 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:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ V_{sph}\ =\ \frac{4}{3}\pi r^3]


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 *[tex \Large r_1] and the other of radius *[tex \Large r_2] then their volumes are in the ratio of:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{V_2}{V_1}\ =\ \frac{\frac{4}{3}\pi \left(r_2\right)^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
*[tex \LARGE e^{i\pi} + 1 = 0]
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