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 \( V = lwh \).