Computing Volume from Cross-Sectional Area

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To compute the volume of the attic, the cross-sectional areas must be analyzed. The attic has a rectangular base of 30 feet by 60 feet and triangular cross sections with a base of 30 feet and height of 10 feet. By slicing the attic into one-foot thick triangular slabs, the volume of each slab can be calculated using the area of the triangle. The total number of slabs corresponds to the height of the attic, which is 10 feet, leading to the overall volume calculation. Understanding the geometry and setting up the integral for the volume is essential for solving the problem accurately.
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Homework Statement


A house attic has rectangular cross sections parallel to the ground and triangular cross sections perpendicular to the ground. The rectangle is 30 feet by 60 feet at the bottom of the attic and the triangles have base 30 feet and height 10 feet. Compute the volume of the attic.


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The Attempt at a Solution



I know how to solve this once it is set up as an integral, but I am having trouble setting up the integral itself.
 
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An integral is overkill. Think of slicing the attic into triangular slabs, each one foot thick. What is the volume of each slab? How many slabs are there?
 

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