10.1.3 Volume of Prisms and Cylinders (continued)
The volume of a regular pentagonal prism is determined in this example. The base edge length and height of the prism are given. To find the volume of the prism, first calculate the area of the base. To find the apothem of the pentagonal base, recognize that the sum of the measures of the interior angles in a pentagon is 540°. The base angle of the triangles with the pentagon’s sides as their base is one-half of 108°, or 54°. The apothem bisects these triangles to form two right triangles with a short leg length of 2 m. The tangent of 54° equals the apothem length over 2 m. The apothem length equals 2tan 54°. Therefore, the base area equals 20tan 54°. Substituting the calculated and given values into the formula for the volume of a prism yields a volume of approximately 275.3 m 3 . The weight of a volume of water contained in a pool in the shape of a rectangular prism is calculated in this application example. The dimensions of the rectangular prism and the density of water are given. First, calculate the volume of the pool by substituting the given dimensions into the formula for the volume of a rectangular prism. The pool contains 30,000 ft 3 of water. Second, convert the volume to gallons using the conversion factor 1 gallon per 0.134 ft 3 . The pool contains 223,881 gallons of water. Finally, convert the gallons of water to pounds of water using the density of water, 8.33 lbs per gallon. The weight of the water is approximately 1,864,929 lbs.
Example 2 Marine Biology Application
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