A right rectangular prism has a length of 8 inches, a width of 3 inches, and a height of 5 inches. What is the volume, in cubic inches, of the prism?
For volume questions involving right rectangular prisms, immediately write the formula , then carefully match each dimension from the problem to , , and . Multiply all three numbers—never add—and use easy groupings (for example, multiply two numbers first to get a simpler product, then multiply by the third). Finally, include units as cubic units (here, cubic inches) to remind yourself it’s a volume.
Hints
Identify the shape
The problem is about a right rectangular prism, which is the 3D shape of a box. Think about how volume is found for such a shape.
Recall the volume formula
For a rectangular prism, volume is the product of its three dimensions. Ask yourself: which numbers in the problem are the three dimensions?
Substitute and multiply
Write the volume formula with the given length, width, and height, then multiply all three numbers together. You can multiply two of them first to make the arithmetic easier.
Desmos Guide
Compute the product
In Desmos, type 8*3*5 into the expression line. The number that Desmos outputs for this expression is the volume of the prism in cubic inches.
Step-by-step Explanation
Recall the volume formula for a rectangular prism
For a right rectangular prism (a box shape), the volume is the product of its three dimensions:
where is length, is width, and is height.
Substitute the given dimensions
You are given:
- length inches
- width inches
- height inches
Substitute these into the formula:
Multiply the dimensions
Now multiply step by step:
- First multiply .
- Then multiply .
So, the volume of the prism is cubic inches.