Question

1. a right rectangular prism is shown below

image of a rectangular prism with length 6 ft, height 3 ft, and width w
the volume of the prism is 90 cubic feet. what is the width, w, in feet, of the prism?
a. 15 ft
b. 5 ft
c. 6 ft
d. 90 ft

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a right rectangular prism is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
From the diagram, we know that \( l = 6 \) ft, \( h = 3 \) ft, and \( V = 90 \) cubic feet. We need to find \( w \).

Step2: Substitute the known values into the formula

Substitute \( V = 90 \), \( l = 6 \), and \( h = 3 \) into the formula \( V = l \times w \times h \):
\[
90 = 6 \times w \times 3
\]

Step3: Simplify the right - hand side of the equation

First, calculate \( 6\times3 = 18 \). So the equation becomes:
\[
90 = 18\times w
\]

Step4: Solve for \( w \)

To find \( w \), we divide both sides of the equation by 18:
\[
w=\frac{90}{18} = 5
\]

Answer:

b. 5 ft