Exercise 29 Page 845

Divide the given solid into a prism and a pyramid.

A unit that is about 13 333 BTUs

Practice makes perfect

An art studio can be modeled by the following composite solid.

Notice that the solid is made of a rectangular prism and a rectangular pyramid, both of the same base and are the same height, h=8 feet. The base is a square with a side of 25 feet.

The area of a square B is calculated by squaring the side. Therefore, B=25^2=625 square feet. Now, let's use the formula for the volume of a prism and for the volume of a pyramid.

Solid	Prism	Pyramid
Base	B= 625	B= 625
Height	h= 8	h= 8
Volume	V_1=Bh=( 625)( 8)=5000	V_2=1/3Bh=1/3( 625)( 8)≈ 1666.67

This tells us that the volume of the prism is V_1=5000 cubic feet, and the volume of the pyramid is V_2≈1666.67 cubic feet. Therefore, the volume of the composite solid is 5000+1666.67=6666.67 cubic feet. Volume of Art Studio: 6666.67 cubic feet To buy a heating unit for the art studio, Sam needs to determine the BTUs (British Thermal Units) required to heat the building. There should be 2 BTUs per cubic foot. Since the volume of the art studio is about 6666.67 cubic feet, Sam needs about 2* 6666.67≈ 13 333 BTUs.

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