Question

Cups A and B are cone shaped and have heights of `16 cm` and `15 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

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

Explanation:

Height and radius of cup A is `h_a=16` cm , `r_a=6` cm

Volume of cup is `1/3*pi*r^2*h :.V_a=1/3*pi*6^2*16` or

`V_a ~~ 603.19` cubic cm.

Height and radius of cup B is `h_b=15` cm , `r_b=4` cm

`:.V_b=1/3*pi*4^2*15 or V_b ~~ 251.33` 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 cup A filled

with water is `r_w/h_w=6/16=3/8 or r_w=(3*h_w)/8`

The volume of water cone is `V_w=251.33` cubic cm.

`:.1/3*pi*r_w^2*h_w =251.33` or

`1/3*pi*((3*h_w)/8)^2*h_w =251.33` or

`h_w^3= (251.33*64)/(3*pi)~~1706.684` or

`h_w= root(3)1706.684 ~~ 11.95(2dp)` cm

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