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Volume of a prism from a pentagonal prism

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The base of a pentagonal prism is regular with an apothem of 4 centimeters. The height of the prism is 16 centimeters. Find the volume of the prism. Round your answer to the nearest cubic centimeter

Guest Apr 6, 2017
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#1
+5576
+3

volume of a prism = area of base * height

Here is a top-down view of the base.

As you can see, it can be split into 5 triangles.

The area of each triangle = (1/2)(2)(4 tan 36º)(4) = 16 tan 36º

So...

the area of the base = 5 * 16 tan 36º = 80 tan 36º

And so..

the volume of the prism = 80 tan 36º * 16 = 1,280 tan 36º ≈ 929.974 cubic cm

hectictar  Apr 6, 2017
#2
+79894
+2

The radius of the pentagon can be found as :

4/sin 54°

And the area of the base  =

5 (1/2) [4/sin(54°)]^2 * sin(72°) =  40 sin (72°) /[sin(54°)]^2

So.....the volume is

Base * Height  =

40 sin (72°) /[sin(54°)]^2 *  16   ≈  929.97 cubic cenimeters = 930 cubic centimeters

CPhill  Apr 6, 2017

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