## Friday, July 19, 2013

### Frustum - Pyramid

Category: Solid Geometry

"Published in Newark, California, USA"

A baking pan has a rectangular base 12 in. by 8 in.; the sides and ends of the pan slope outward, so that the upper edges measure respectively 13 ½ in. by 9 in. Find the volume of a baking pan if the depth of the pan is 2 in. Find the amount of cake batter required to fill the pan to one-half its depth.

Solution:

To illustrate the problem, it is better to draw the figure as follows

 Photo by Math Principles in Everyday Life

The area of the upper base is calculated as follows

The area of the lower base is calculated as follows

The volume of a baking pan or a frustum of a pyramid is calculated as follows

If a baking pan is filled with a cake batter one-half of its depth which is 1 in., the volume of a cake batter is calculated as follows

 Photo by Math Principles in Everyday Life

The area of the bottom of a baking pan is the same as the bottom of a cake batter which is A2 = 96 in2.

The length of the top of a cake batter is calculated using similar triangles

 Photo by Math Principles in Everyday Life

The width of the top of a cake batter is calculated using similar triangles

 Photo by Math Principles in Everyday Life

The area of the top of a cake batter is

Therefore, the volume of a cake batter is