Question

Cups A and B are cone shaped and have heights of `37 cm` and `27 cm` and openings with radii of `9 cm` and `4 cm`, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Answer 1

Will not overflow and it has a height of `5 1/3`cm

Explanation:

Volume of the cone is given by `1/3pitimesr^2timesh`
where h is the height and r is the radius

Volume of Cup B: `1/3pir^2h = 1/3pitimes4^2times27 = 144pi`

Volume of Cup A: `1/3pir^2h = 1/3pitimes9^2times37 = 999pi`

Therefore, Cup A will not overflow

Now, we need to find the height of Cup A

`1/3pir^2h = 144pi`

`1/3pitimes9^2timesh=144pi`

`27pih=144pi`

`h=5 1/3`cm