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?

1 Answer
Jun 28, 2016

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