Question

Cups A and B are cone shaped and have heights of `27 cm` and `24 cm` and openings with radii of `7 cm` and `14 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

Since volume of contents in cup A `(1385.44)` c.cm is less than that of cup B `(4926.02)` c.cm , cup A will overflow.

Explanation:

Height and radius of cup A is `h_a=27` cm ,`r_a=7` cm

Volume of cone is `1/3*pi*r^2*h :.V_a=1/3*pi*7^2*27` or

`V_a ~~ 1385.44` cubic cm.

Height and radius of cup B is `h_b=24` cm,`r_b=14` cm

`:.V_b=1/3*pi*14^2*24 or V_b ~~ 4926.02` cubic cm.

Since `V_a < V_b` , the content will overflow. [Ans]