A rectangular prism has a volume of 288 cubic centimeters. If the area of the base is 12 square centimeters, what is the height of the prism?
Understand the Problem
The question provides the volume and base area of a rectangular prism and asks to calculate its height. We can use the formula Volume = Base Area * Height to find the height.
Answer
24 centimeters
Answer for screen readers
24 centimeters
Steps to Solve
- Recall the formula for the volume of a rectangular prism
The volume $V$ of a rectangular prism is given by the formula $V = B \times h$, where $B$ is the area of the base and $h$ is the height.
- Substitute the known values into the formula
We are given that the volume $V = 288$ cubic centimeters and the base area $B = 12$ square centimeters. Substituting these values into the formula, we get $288 = 12 \times h$.
- Solve for the height $h$
To find the height $h$, we need to isolate it by dividing both sides of the equation by 12:
$h = \frac{288}{12}$
$h = 24$
Therefore, the height of the prism is 24 centimeters.
24 centimeters
More Information
The height of the prism is 24 cm. A prism is a polyhedron with two congruent and parallel faces (bases) and whose lateral faces are parallelograms.
Tips
A common mistake is to multiply the volume and base area instead of dividing. Another mistake could be using the wrong formula for the volume of a rectangular prism e.g. including length and width separately instead of using the base area.
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