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?

1 Answer
Feb 6, 2018

See a solution process below:

Explanation:

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