Question

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?

Answer 1

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