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?

1 Answer
Mar 13, 2016

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 "#