"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
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| Photo by Math Principles in Everyday Life |
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
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| 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
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| Photo by Math Principles in Everyday Life |
The width of the top of a cake batter is calculated using similar triangles
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| 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
