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?

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Answer 1 · 2018-06-04T02:03:10

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

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

Cups A and B are cone shaped and have heights of 37 cm37 cm and 27 cm27 cm and openings with radii of 9 cm9 cm and 4 cm4 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?