Cups A and B are cone shaped and have heights of $27 cm$ and $24 cm$ and openings with radii of $7 cm$ 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 · 2018-02-06T21:15:34

See a solution process below:

The formula for the volume of a cone is:

$V = pir^2h/3$

The Volume of cup A is:

$V_a = pi xx (7"cm")^2 xx (27"cm")/3$

$V_a = pi xx 49"cm"^2 xx 9"cm"$

$V_a = pi xx 441"cm"^3$

$V_a = 441"cm"^3pi$

The Volume of cup B is:

$V_a = pi xx (9"cm")^2 xx (24"cm")/3$

$V_a = pi xx 81"cm"^2 xx 8"cm"$

$V_a = pi xx 648"cm"^3$

$V_a = 648"cm"^3pi$

If a full Cup B is poured into an empty Cup A, then Cup A will overflow

Cups A and B are cone shaped and have heights of 27 cm27 cm and 24 cm24 cm and openings with radii of 7 cm7 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?