Cups A and B are cone shaped and have heights of $32 cm$ and $21 cm$ and openings with radii of $15 cm$ and $9 cm$ , 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 · 2018-07-14T04:23:57

Cup A will be filled to a height of $7.56cm$

Volume of Cup B
= $1/3pir^2h$
= $1/3pitimes9^2times21$
= $567pi$

Volume of Cup A
= $1/3pir^2h$
= $1/3pitimes15^2times32$
= $2400pi$

If Cup B is poured into Cup A, the cup will not overflow. To find the height of water in Cup A,

$1/3pitimes15^2h=567pi$

$(225h)/3=567$

$h=(567times3)/225$

$h=7.56$

Cups A and B are cone shaped and have heights of 32 cm32 cm and 21 cm21 cm and openings with radii of 15 cm15 cm and 9 cm9 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?