Cups A and B are cone shaped and have heights of 24 cm and 26 cm and openings with radii of 11 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 20, 2016
no overflow , h ≈ 17.4cm
Explanation:
The volume of a cone =
1/3pir^2h where r is the radius and h , the height
Use this to calculate volumes of A and B
V_A = 1/3pixx11^2xx24 ≈ 3041.06" cubic cm "
V_B = 1/3pixx9^2xx26 ≈ 2205.40" cubic cm " since
V_B < V_A" there will be no overflow " Volume of liquid in cup A will be that of cup B
rArr 1/3pixx11^2h = 2205.4
rArr h = 2205.4/(1/3pixx11^2) ≈ 17.4"cm"
