Question

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?

Answer 1

`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]