Hi, I’m having some trouble with a math question and I was wondering if you could help me.

Here it is:

A regular drinking cup has a circular lower base 8 cm in diameter, a lip 12 cm in diameter, and a height of 10 cm. What is its volume?

Thanks very much.

as You can see by the drawing, the cup is turned upside down and extended

to a cone.  The height, radius and sides of the cones form two right triangles which are similar.

This means that the sides are proportional so we set up the equation:

(x+10)/6  =  x/4 which, when solved,  gives x = 20. So the height of the

small triangle is  20 and the height of the larger triangle is 20+10 or 30.

The cup that you want to determine the volume of is the difference of the volume of the large cone and the volume of the small cone.  That has been computed below.   Enjoy!

cone1.gif (5861 bytes)

 

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