Question

Cups A and B are cone shaped and have heights of `38 cm` and `37 cm` and openings with radii of `12 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 ≈ 20.81cm

Explanation:

The volume of a cone is found by using

`V = 1/3pir^2h" where r is radius and h , the height "`

calculate the volumes of A and B

`V_A = 1/3pixx12^2xx38 ≈ 5730.265" cubic cm "`

`V_B = 1/3pixx9^2xx37 ≈ 3138.451" cubic cm "`

since volume of A > volume of B then no overflow

and the volume of liquid in A = 3138.451 (from B)

so `1/3pixx12^2xxh = 3138.451`

`rArr h = 3138.451/(1/3pixx12^2) ≈ 20.81 cm "`