There is a sphere that has a radius of 9 inches. The sphere has a smaller sphere inside that has a radius of 3 inches. What is the ratio of the volume of the small sphere to the volume of the larger sphere?

Question

jim_thompson5910 · Answer

What is the volume of the larger sphere?

anonymous · Answer

you dont know it

jim_thompson5910 · Answer

Are you able to find it?

anonymous · Answer

I dont know how

jim_thompson5910 · Answer

You would use the formula

$$\Large V = \frac{4}{3}\pi*r^3$$

jim_thompson5910 · Answer

for the larger sphere, r = 9
the smaller one, r = 3

anonymous · Answer

So it would be  V= 4/3 pie (729)

how would you multiply 4/3

jim_thompson5910 · Answer

think of 729 as 729/1

jim_thompson5910 · Answer

so (4/3)*729 = (4/3)*(729/1) = (4*729)/(3*1) = 2916/3 = 972

anonymous · Answer

ohh! ok thank you!

jim_thompson5910 · Answer

meaning that 

$$\Large V = \frac{4}{3}\pi*(729)$$

becomes

$$\Large V = 972\pi$$

jim_thompson5910 · Answer

do the same for the smaller sphere, then you'll have your ratio (but don't forget to fully reduce this ratio)

anonymous · Answer

what would the ratio be to find the surface area of the two spheres?

jim_thompson5910 · Answer

what did you get for the ratio of the volumes?

anonymous · Answer

27 over 1, and the pie cancels out

jim_thompson5910 · Answer

they want it in the form (small volume):(large volume) and you reduce that

jim_thompson5910 · Answer

so that ratio would be 1:27 when fully reduced

jim_thompson5910 · Answer

as for the surface area, you use the formula

$$\Large SA = 4\pi*r^2$$

anonymous · Answer

oh yes I switched the rations, and ok thanks i will use that for SA