Cups A and B are cone shaped and have heights of 39 cm and 22 cm and openings with radii of 17 cm and 11 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 ≈ 9.211cm
Explanation:
The volume of a cone
= 1/3pir^2h where r is the radius and h , the height.
Use this to calculate the volumes of A and B.
V_A = 1/3pixx17^2xx39 ≈ 11802.96" cubic cm "
V_B = 1/3pixx11^2xx22 ≈ 2787.64" cubic cm " Since
V_B < V_A" there will be no overflow " The volume of liquid in cup A will be that of cup B.
hence
1/3pixx17^2h = 2787.64 multiply both sides by 3 to eliminate feaction
thus
pixx17^2h = (3xx2787.64) and h
= (3xx2787.64)/(pixx17^2) ≈ 9.21"cm"
