Question

Cups A and B are cone shaped and have heights of `33 cm` and `26 cm` and openings with radii of `13 cm` and `8 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 ≈ 9.85 cm

Explanation:

The first step is to calculate the volume of the 2 cups using

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

where r is the radius and h , the height.

`V_A = 1/3pixx13^2xx33 ≈ 5840.22" cubic cm "`

`V_B = 1/3pixx8^2xx26 ≈ 1742.54" cubic cm "`

Since `V_A > V_B " there will be no overflow "`

The volume of liquid in A will therefore be 1742.54 cubic cm

`rArr 1/3pixx13^2xxh = 1742.54`

`rArr h = (1742.54)/(1/3pixx13^2) ≈ 9.85"cm"`