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mojhsa [17]
2 years ago
14

What is the volume of the right triangular prism in cubic meters? Round to the nearest cubic meter

Mathematics
1 answer:
Harlamova29_29 [7]2 years ago
4 0

This question is incomplete because it lacks the diagram of the right triangular prism. Find attached to this answer, the diagram

Answer:

1771m³ or 1771 cubic meters

Step-by-step explanation:

Formula for the volume of Right triangular prism =

1/2 × base × height × Length

From the attached diagram,

We can see that the

Height of the prism = 23m

Base of the prism = 14m

Width or length of the prism = 11m

Volume = 1/2 × 14m × 23m × 11m

Volume of the right triangular prism = 1771m³ or 1771 cubic meters

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The formula is given as;

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This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.

Therefore, we would have;

\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}

Therefore, if the order is relevant, this selection can be done in 6,720 ways.

(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;

_nC_r=\frac{n!}{(n-r)!r!}

The formula can now be applied as follows;

\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}

If the order is not relevant, then the selection can be done in 56 ways.

3 0
10 months ago
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Step-by-step explanation:

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Step-by-step explanation:

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I hope this was helpful.

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2 years ago
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