A prism has a rectangle for a base. The area of the rectangle is square yards and the height of the prism is yards. What is the volume of the prism?
Understand the Problem
The question provides the area of the rectangular base of a prism and the height of the prism. It asks to find the volume of the prism. The formula for the volume of a prism is Volume = Base Area * Height.
Answer
$V = 40 \text{ cm}^3$
Answer for screen readers
$V = 40 \text{ cm}^3$
Steps to Solve
- Write down the formula for the volume of a prism
The volume $V$ of a prism is given by the formula: $$V = B \cdot h$$ where $B$ is the area of the base and $h$ is the height of the prism.
- Substitute the given values into the formula
We are given that the area of the rectangular base $B = 4 \text{ cm}^2$ and the height of the prism $h = 10 \text{ cm}$. Substituting these values into the formula, we get: $$V = 4 \text{ cm}^2 \cdot 10 \text{ cm}$$
- Calculate the volume
Multiplying the values, we find the volume: $$V = 40 \text{ cm}^3$$
$V = 40 \text{ cm}^3$
More Information
The volume of a prism is measured in cubic units, which in this case are $\text{cm}^3$. This represents the amount of space the prism occupies.
Tips
A common mistake is to confuse the area of the base with the length of a side of the base. Remember that the problem provides the area of the base directly, so you don't need to calculate it from side lengths. Another common mistake is using the wrong units or forgetting to include units in the final answer. The volume should be in cubic units because it's a three-dimensional measurement.
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