Cups A and B are cone shaped and have heights of #12 cm# and #18 cm# and openings with radii of #6 cm# and #4 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
Apr 9, 2018

#10.48# cm high of cup A will be filled

Explanation:

Height and radius of cup A is #h_a=12 cm , r_a=6# cm

Volume om cone is #1/3*pi*r^2*h :.V_a=1/3*pi*6^2*12# or

#V_a~~ 452.39# cubic cm.

Height and radius of cup B is #h_b=18# cm ,# r_b=4# cm

# :.V_b=1/3*pi*4^2*18 or V_b~~ 301.59# cubic cm.

Since #V_a > V_b # , the content will not overflow.

The ratio of radius and hight of cup A is

#r/h=6/12 =1/2 #. The ratio of radius and hight of water cone

is #r_w/h_w=1/2 or r_w=h_w/2#

The volume of water cone is #V_w=301.59# cubic cm.

#:.1/3*pi*r_w^2*h_w =301.59# or

# 1/3*pi*(h_w/2)^2*h_w =301.59# or

#h_w^3= (301.59*12)/pi~~1151.99# or

#h_w= root(3)1151.99 ~~ 10.48 (2dp)# cm

#10.48# cm high of cup A will be filled [Ans]