Question

Question 13 Find the volume of the prism.

Answer 1

Answer:

volume of the prism=(1/2×9×6)×12

=27×12

=324 cm³

Answer 2

Answer:

$\boxed {\boxed {\sf B. \ 324 \ cm^3}}$

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).

$V= B*h$

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

$B= \frac{1}{2} b*h$

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

• b= 6 cm
• h= 9 cm

$B= \frac{1}{2} (6 \ cm)(9 \ cm)$

Multiply the numbers in parentheses.

$B= \frac{1}{2}(54 \ cm^2)$

Multiply by 1/2 or divide by 2.

$B= 27 \ cm^2$

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.

$V= 27 \ cm^2 * 12 \ cm$

Multiply.

$V= 324 \ cm^3$

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