# 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" #