Question

Cups A and B are cone shaped and have heights of `32 cm` and `21 cm` and openings with radii of `13 cm` and `11 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 B contents when poured into cup A will not cause overflow. cup A will be filled up `15.0355 Cm`

Explanation:

Volume of cone is `1/3*pi*r^2*h` where r is radius and h is height.

Cup A:

Given `r = 13` and `h = 32`.

Volume of cup A is `1/3*pi*13^2*32 =` `5663.24 Cm^3`

Cup B:

Given `r = 11` and `h = 21`.

Volume of cup B is `1/3*pi*11^2*21 =` `2660.91 Cm^3`

As volume of cup B is less than cup A, when the full contents of cup B are poured into cup A, it will not overflow.

The filled portion in cup A is also in the form of a cone. To determine how high it is, assume height=h and radius = 13 for the filled cone part.

Volume = `1/3*pi*13^2*h` = `2660.91 Cm^3`

`h = 2660.91/(1/3*13^2*pi) = 15.0355 Cm`