Cups A and B are cone shaped and have heights of 32 cm and 16 cm and openings with radii of 15 cm and 12 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?

1 Answer
sjc
Aug 20, 2017

Cup A will not overflow

4.76cm" "high from the bottom of the cup

Explanation:

V_("cone")=1/3pir^2h

where" "r="the base radius of the cone ",

"and "h="the perpendicular height of the cone"

we have cups a & B

Cup A" "r=15cm,h=32cm

Cup B" "r=12cm, h=16cm

first we find the two volumes

V_A=1/3pi15^2xx32

V_A=2400picm^3

V_B=1/3pi12^2xx16
V_B=768picm^3

now cup B is full and poured into cup A

we see

V_B < V_A

so cup A will not overflow

how high up will A be filled.

using the volume formula once more

V_(A')=1/3pir^2h

where h is the height from the base of the cone

that is from the top of the cup

768cancel(pi)=1/3cancel(pi)15^2h

h=(768xx3)/15^2=10.24cm

from the bottom of the cup

H=15-10.24=4.76cm

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