Cups A and B are cone shaped and have heights of $35 cm$ and $24 cm$ and openings with radii of $9 cm$ and $11 cm$ , 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 · 2018-07-22T21:58:00

Cup A will overflow

The volume ( $V_A$ ) of cone cup-A with vertical height $35$ cm & radius $9$ cm is

$V_A=1/3\pi r^2h=1/3\pi(9^2)(35)=945\pi\ cm^3$

The volume ( $V_B$ ) of cone cup-B with vertical height $24$ cm & radius $11$ cm is

$V_B=1/3\pi r^2h=1/3\pi(11^2)(24)=968\pi\ cm^3$

Since, the volume of cone cup B is more than that of cone cup A

$V_B>V_A$

hence when the content of full cup B is poured into cup A, cup A would overflow.

Cups A and B are cone shaped and have heights of 35 cm35 cm and 24 cm24 cm and openings with radii of 9 cm9 cm and 11 cm11 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?