Two similar cones have lateral areas of 27pi and 48pi. What is the ratio of their volumes?

Question

anonymous · Answer

first find the ratio of their lateral areas...ration always means a fraction

$$\frac{27\pi}{48\pi} = \frac{9}{16}$$

area ratios are always squares and volume ratios are always cubes of the linear (side) ratios

so if the lateral *area* ratio is 9/16, what is the square root of 9/16? (to get the side length ratio)

anonymous · Answer

9/16 is not your answer...

anonymous · Answer

I know … I have to square root 9:16 which gives me 3:4 then to find the volume I cube the ratios!  Right? so the answer is 27:64.

anonymous · Answer

exactly...just wanted to make sure you got to the end :)

anonymous · Answer

Thank you! :)