The volume of a right rectangular prism is 96 cubic inches. The base of the prism is a rectangle with length inches and width inches. What is the height, in inches, of the prism?
For volume questions with rectangular prisms, start by writing the standard formula . Plug in the known values, then combine the length and width to get the area of the base. Finally, isolate the unknown (usually the height) by dividing the volume by the base area. Keeping the steps in this order prevents common mistakes like forgetting one dimension or using addition instead of multiplication.
Hints
Recall the volume formula
What is the formula for the volume of a rectangular prism in terms of its length, width, and height?
Use the given dimensions
You know the volume, the length (8 inches), and the width (4 inches). Plug these into the volume formula and write an equation involving the height .
Isolate the height
Once you multiply the length and width, how can you use division to solve for in your equation?
Desmos Guide
Compute the height directly
In the expression line, type 96/(8*4) and press Enter. The value that Desmos outputs is the height of the prism in inches.
Step-by-step Explanation
Write the volume formula
For a right rectangular prism,
where is volume, is length, is width, and is height.
Substitute the known values
You are given:
- Volume cubic inches
- Length inches
- Width inches
Substitute into the formula:
Simplify the base area
First multiply the length and width:
So the equation becomes:
Solve for the height
To find , divide both sides of the equation by :
So , meaning the height of the prism is 3 inches.