Question

given this rectangular prism with length = 1.2 m, height = 1.3 m, and volume = 3.276 m³, find the missing width of the prism:

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height. We need to solve for \( w \), so we can rearrange the formula to \( w=\frac{V}{l\times h} \).

Step2: Substitute the given values into the formula

We know that \( V = 3.276 \, \text{m}^3 \), \( l = 1.2 \, \text{m} \), and \( h = 1.3 \, \text{m} \). First, calculate the product of \( l \) and \( h \): \( l\times h=1.2\times1.3 = 1.56 \, \text{m}^2 \).

Step3: Calculate the width

Now, substitute \( V \) and \( l\times h \) into the formula for \( w \): \( w=\frac{3.276}{1.56} \). Performing the division, we get \( w = 2.1 \, \text{m} \).

Answer:

The missing width of the rectangular prism is \( 2.1 \, \text{m} \).