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 "
