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Mnenie [13.5K]
3 years ago
14

Please i need help on finding the volume

Mathematics
1 answer:
SpyIntel [72]3 years ago
3 0

Answer:

Volume =  516.1425 cubic feet

Step-by-step explanation:

The pentagon base appears regular.  so every side is 10 feet in length.

Now we need to figure out the area of the pentagonal base in order to find volume.

Volume V = (pentagon base area)*height

I need to find the apothem length as indicated in the drawing.

call it "a"

360/5 =  72 degrees.

36 degrees.

5/a = tan 36 ,    a =  5/(tan 36) = 6.88190  feet.

Area of pentagon base =  5 *  (1/2)*10* a  =  5*(1/2)*10* 6.88190 =172.0475 sq. ft

Area of pentagon base =  =172.0475 sq. ft

V = 172.0475 * 3 = 516.1425 cubic feet

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It is sometimes helpful to start from what you are given and see what develops.

Here, angle B is 30°. That means angle CAB is 60° (the acute angles of a right triangle are complements). AL bisects that 60° angle, meaning two things:

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