Question

Cups A and B are cone shaped and have heights of `28 cm` and `23 cm` and openings with radii of `11 cm` and `9 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 be filled upto 15.3967 cm

Explanation:

Volume of cone B `V_b= (1/3) pi r_2^2 h_2`

Given `r_2 = 9 cm, h_2 = 23 cm`

`V_b = (1/3) * pi * 9^2 * 23 = 1950.929 pi` `cm^3`

Similarly Volume of cone A `V_a = (1/3) pi r_1^2 h_1`

Given `r-1 = 11 cm, h_1 = 28 cm`

`V_a = (1/3) * pi * 11^2 * 37 = 3547.9053 pi` `cm^3`

As volume of cone A is greater than the volume of cone B, cup A will not overflow.

Volume of partly filled cone A `V_p = (1/3) pi r_1^2 h_3`

`V_p = = V_b`

`(1/3) pi * 9^2 * 23 = (1/3) * pi * 11^2 * h_3`

`h_3 = (cancel((1/3) * pi) * 9^2 * 23) / (cancel((1/3) * pi) * 11^2)`

`h_3 =( 1863) / 121 = 15.3967` `cm`