Cups A and B are cone shaped and have heights of $32 cm$ and $24 cm$ and openings with radii of $9 cm$ and $5 cm$ , 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 · 2018-07-14T06:42:35

$7.41cm$

Volume of Cup A
$V=1/3pir^2h$
$V=1/3pitimes9^2times32$
$V=864pi$

Volume of Cup B
$V=1/3pir^2h$
$V=1/3pitimes5^2times24$
$V=200pi$

If Cup B was poured into Cup A, then Cup A will not overflow since it can hold a volume of $864pi$

To find the height of of water in Cup A,
$1/3pitimes9^2h=200pi$
$27pih=200pi$
$27h=200$
$h=200/27=7.41cm$

Cups A and B are cone shaped and have heights of 32 cm32 cm and 24 cm24 cm and openings with radii of 9 cm9 cm and 5 cm5 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?