Question

The formula for the volume of a rectangular solid is V=lwh where l is the length,w is the width, and h is the height. Which equations are equivalent to the formula for the volume of a rectangular solid?

Answer 1

To find equations that are equivalent to the formula for the volume of a rectangular solid, \( V = lwh \), we can manipulate the original equation in several ways without changing its meaning. Here are a few equivalent forms:

1. **Rearranging for length**:
\( l = \frac{V}{wh} \)

2. **Rearranging for width**:
\( w = \frac{V}{lh} \)

3. **Rearranging for height**:
\( h = \frac{V}{lw} \)

4. **Using multiplication in a different order** (due to the commutative property of multiplication):
\( V = wlh \)
\( V = hlw \)
\( V = whl \)

5. **Expressing volume in terms of a product form**:
\( V = (lh)w \)
\( V = (lw)h \)
\( V = (wh)l \)

Any of these rearrangements or forms maintain the same mathematical relationship and thus are considered equivalent to \( V = lwh \).