PrinceHuncho
Answered

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Question 13
Find the volume of the prism.

Question 13 Find The Volume Of The Prism class=

Sagot :

senalvidun

Answer:

volume of the prism=(1/2×9×6)×12

=27×12

=324 cm³

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf B. \ 324 \ cm^3}}[/tex]

Step-by-step explanation:

The volume of a triangular prism is the product of the area of the triangular cross-section (B) and the height (h).

[tex]V= B*h[/tex]

First, let's find the area of the triangular cross-section/the end of the triangle. The area of a triangle is:

[tex]B= \frac{1}{2} b*h[/tex]

The base of the triangle base (not the prism) is 6 centimeters and the height is 9 centimeters.

  • b= 6 cm
  • h= 9 cm

[tex]B= \frac{1}{2} (6 \ cm)(9 \ cm)[/tex]

Multiply the numbers in parentheses.

[tex]B= \frac{1}{2}(54 \ cm^2)[/tex]

Multiply by 1/2 or divide by 2.

[tex]B= 27 \ cm^2[/tex]

Now we know the area of the cross-section or base is 27 square inches. The height of the prism is 12 centimeters.

  • B= 27 cm²
  • h= 12 cm

Substitute the values into the volume formula for a triangular prism.

[tex]V= 27 \ cm^2 * 12 \ cm[/tex]

Multiply.

[tex]V= 324 \ cm^3[/tex]

The volume of the prism is 324 cubic centimeters and choice B is correct.

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