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vova2212 [387]
3 years ago
15

A pentagonal prism has a height of 9 feet, and each base edge is 3 feet. Find the volume. Round your answer to the nearest hundr

edth.
Mathematics
2 answers:
Andrej [43]3 years ago
7 0
The volume is 139.36ft^3
OLga [1]3 years ago
5 0

Height of the pentagon = 9 ft

Edge of base = 3 ft

area of pentagon = \frac{s^{2}n}{4 tan\left ( \frac{180}{n} \right )}

s is the length of any side = 3

n is the number of sides = 5

tan is the tangent function calculated in degrees

\\ \\\\area of pentagon = \frac{3^{2}(5)}{4 tan\left ( \frac{180}{5} \right )}\\\\\\area of pentagon = \frac{9(5)}{4 tan\left ( 36 \right )}\\\\area of pentagon = \frac{45}{4  ( 0.7265 )}\\\\area of pentagon = \frac{45}{2.906}\\\\area of pentagon = 15.4852

Volume of the pentagon = area of base (height )

Volume of the pentagon = 15.4852 (9)

Volume of the pentagon = 139.366

Volume of the pentagon = 139.37 cu.ft


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Binomial probability distribution

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P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

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And \pi is the probability of X happening.

A probability is said to be unusually low if it is lower than 5%.

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