Question

Cups A and B are cone shaped and have heights of `32 cm` and `27 cm` and openings with radii of `12 cm` and `13 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

`31.9` cm high of cup A will be filled.

Explanation:

Height and radius of cup A is `h_a=32 cm , r_a=12` cm

Volume om cone is `1/3*pi*r^2*h :.V_a=1/3*pi*12^2*32` or

`V_a= 4825.49` cubic cm.

Height and radius of cup B is `h_b=27 cm , r_b=13` cm

`:.V_b=1/3*pi*13^2*27 or V_b= 4778.36` cubic cm.

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

The ratio of radius and hight of cup A is

`r/h=12/32 =3/8`. The ratio of radius and hight of water cone

is `r_w/h_w=3/8 or r_w=(3*h_w)/8`

. The volume of water cone is `V_w=4778.36` cubic cm.

`:.1/3*pi*r_w^2*h_w =4778.36` or

`1/3*pi*((3*h_w)/8)^2*h_w =4778.36` or

`h_w^3= (4778.36*64)/(3*pi)~~32447.9835` or

`h_w= root(3)32447.9835 ~~ 31.90(2dp)` cm

`31.9` cm high of cup A will be filled [Ans]