Question

q: what is the volume (in cm³) of a triangular prism with base 3 and height 6 and length 8?

Explanation:

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

The volume \( V \) of a triangular prism is given by the formula \( V=\text{Area of the triangular base} \times \text{length of the prism} \). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).

Step2: Calculate the area of the triangular base.

Given the base of the triangle \( b = 3\space\text{cm} \) and the height of the triangle \( h = 6\space\text{cm} \). The area of the triangle \( A=\frac{1}{2}\times b\times h=\frac{1}{2}\times3\times6 \).
Calculating this, \( \frac{1}{2}\times3\times6 = 9\space\text{cm}^2 \).

Step3: Calculate the volume of the triangular prism.

The length of the prism \( l = 8\space\text{cm} \). Using the volume formula for the prism \( V = A\times l \), we substitute \( A = 9\space\text{cm}^2 \) and \( l = 8\space\text{cm} \). So \( V=9\times8 \).
Calculating this, \( 9\times8=72\space\text{cm}^3 \).

Answer:

The volume of the triangular prism is \( 72\space\text{cubic centimeters} \) (or \( 72\space\text{cm}^3 \)).