Question

the volume of a rectangular prism is 117.8 m³. the prism has a base that is 3.8 m by 3.1 m. find the height of the prism. the height of the rectangular prism is meters.

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 can rearrange this formula to solve for \( h \): \( h=\frac{V}{l\times w} \).

Step2: Identify the given values.

We know that \( V = 117.8\space m^3 \), \( l = 3.8\space m \), and \( w = 3.1\space m \). First, calculate the area of the base \( B=l\times w \). So, \( B = 3.8\times3.1 \). Let's compute that: \( 3.8\times3.1 = 11.78\space m^2 \).

Step3: Solve for the height.

Now, substitute \( V \) and \( B \) into the formula for \( h \): \( h=\frac{V}{B}=\frac{117.8}{11.78} \). Dividing these values, we get \( h = 10 \).

Answer:

10