Question

Cups A and B are cone shaped and have heights of `34 cm` and `27 cm` and openings with radii of `11 cm` and `5 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

Cup A will not overflow. It will be filled up to `color(violet)(5.58 cm)` height

Explanation:

Cone A `r_a = 11 cm, h_a = 34 cm`

Cone B `r_b = 5 cm, h_b = 27 cm`

Volume of Cone A `V_a = (1/3) pi (r_a)^2 h_a`

`V_a = (1/3) pi * 11^2 * 34 = 4308.17 cm^3`

Volume of Cone A `V_b = (1/3) pi (r_b)^2 h_b`

`V_a = (1/3) pi * 5^2 * 27 = 706.86 cm^3`

Since `V_b < V_a`, it will not overflow.

`(1/3) pi (r_a)^2 * h = V_b = 225 pi`

`h = (3 * 225 * pi) / (pi * 11^2) = 5.58 cm`