Question

what is the volume of the following triangular prism? 9 m 6 m 13 m 351 m³ 380 m³ 398 m³ 327 m³ question 21 (5 points) listen what is the volume of a rectangular prism that is 4 ft. by 12 ft. by 6 ft.? 288 ft.³ 324 ft.³ 315 ft.³ 205 ft³

Explanation:

First Question (Triangular Prism Volume)

Step1: Recall the formula for the volume of a triangular prism.

The volume \( V \) of a triangular prism is given by \( V = \text{Area of the triangular base} \times \text{length of the prism} \). The triangular base is a right triangle with base \( b = 9 \, \text{m} \) and height \( h = 6 \, \text{m} \), and the length of the prism (the distance along the direction perpendicular to the triangular base) is \( l = 13 \, \text{m} \).

Step2: Calculate the area of the triangular base.

The area of a right triangle is \( \frac{1}{2} \times b \times h \). Substituting \( b = 9 \, \text{m} \) and \( h = 6 \, \text{m} \), we get:
\[
\text{Area of base} = \frac{1}{2} \times 9 \times 6 = \frac{54}{2} = 27 \, \text{m}^2
\]

Step3: Calculate the volume of the triangular prism.

Now, multiply the area of the base by the length of the prism (\( l = 13 \, \text{m} \)):
\[
V = 27 \times 13 = 351 \, \text{m}^3
\]

Step1: Recall the formula for the volume of a rectangular prism.

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \), \( w \), and \( h \) are the length, width, and height respectively.

Step2: Substitute the given values.

Here, \( l = 4 \, \text{ft} \), \( w = 12 \, \text{ft} \), and \( h = 6 \, \text{ft} \). Substituting these into the formula:
\[
V = 4 \times 12 \times 6
\]

Step3: Perform the multiplication.

First, multiply \( 4 \times 12 = 48 \), then multiply \( 48 \times 6 = 288 \, \text{ft}^3 \).

Answer:

351 \( \text{m}^3 \) (corresponding to the option: 351 \( \text{m}^3 \))

Second Question (Rectangular Prism Volume)