Question

Cups A and B are cone shaped and have heights of `25 cm` and `18 cm` and openings with radii of `8 cm` and `3 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 ≈ 2.53cm

Explanation:

Volume (V) of cone `= 1/3pir^2h`

hence `V_A = 1/3pixx8^2xx25 ≈ 1675.516" cubic cm"`

and `V_B = 1/3pixx3^2xx18 ≈ 169.646" cubic cm "`

When B is poured into A ,no overflow since `V_B < V_A`

The volume of liquid in A = 169.646

To find height of liquid solve:

`1/3pixx8^2xxh = 169.646`

multiply by 3 to eliminate fraction.

`rArr pixx64xxh =(3xx169.646) rArr h = (3xx169.646)/(64pi) ≈ 2.53`