Question

Cups A and B are cone shaped and have heights of `24 cm` and `26 cm` and openings with radii of `11 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

no overflow , h ≈ 17.4cm

Explanation:

The volume of a cone = `1/3pir^2h`

where r is the radius and h , the height

Use this to calculate volumes of A and B

`V_A = 1/3pixx11^2xx24 ≈ 3041.06" cubic cm "`

`V_B = 1/3pixx9^2xx26 ≈ 2205.40" cubic cm "`

since `V_B < V_A" there will be no overflow "`

Volume of liquid in cup A will be that of cup B

`rArr 1/3pixx11^2h = 2205.4`

`rArr h = 2205.4/(1/3pixx11^2) ≈ 17.4"cm"`