Question

Cups A and B are cone shaped and have heights of `39 cm` and `22 cm` and openings with radii of `17 cm` and `11 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 ≈ 9.211cm

Explanation:

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

where r is the radius and h , the height.

Use this to calculate the volumes of A and B.

`V_A = 1/3pixx17^2xx39 ≈ 11802.96" cubic cm "`

`V_B = 1/3pixx11^2xx22 ≈ 2787.64" cubic cm "`

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

The volume of liquid in cup A will be that of cup B.

hence `1/3pixx17^2h = 2787.64`

multiply both sides by 3 to eliminate feaction

thus `pixx17^2h = (3xx2787.64)`

and h `= (3xx2787.64)/(pixx17^2) ≈ 9.21"cm"`