We can calculate the volume $V$ of a rectangular prism using $V=\ell w h$, where $\ell$ is the length, $w$ is the width, and $h$ is the height of the prism. Suppose that a prism has a volume of $200 \mathrm{~cm}^{3}$ and $\ell=2 w$.
a. Rewrite the volume formula by making substitutions for $V$ and $\ell$.
Type the answer in the box below.
b. Rewrite the equation as $h$ in terms of $w$. (Turn it into $h=$ something.)
Type the answer in the box below.
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h=
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Answer
Simplify the equation to get the final answer: \(\boxed{h = \frac{100}{w^2}}\)
Step 1 ：Substitute the given values into the volume formula: \(200 = 2w^2h\)
Step 2 ：Isolate h by dividing both sides by \(2w^2\): \(h = \frac{200}{2w^2}\)
Step 3 ：Simplify the equation to get the final answer: \(\boxed{h = \frac{100}{w^2}}\)
