Question

The volume of a prism is given by the formula V=lwh
, where l
is the length, w
is the width, and h
is the height of the prism. (2 points)
a. Solve the formula for w
.

w=

b. A prism has a volume of 504 cubic feet, a length of 7 feet, and a height of 12 feet. What is the width of the prism, rounded to the nearest foot?

w=
ft

Answer 1

a. To solve the formula \( V = lwh \) for \( w \), we can rearrange the formula as follows:

1. Start with the formula:
\[
V = lwh
\]

2. Divide both sides by \( lh \) to isolate \( w \):
\[
w = \frac{V}{lh}
\]

So, the solved formula for \( w \) is:
\[
w = \frac{V}{lh}
\]

b. Given that the volume \( V = 504 \) cubic feet, the length \( l = 7 \) feet, and the height \( h = 12 \) feet, we can plug these values into the formula we derived:

1. Substitute the values into the formula:
\[
w = \frac{504}{7 \times 12}
\]

2. Calculate \( 7 \times 12 \):
\[
7 \times 12 = 84
\]

3. Now substitute this back into the equation for \( w \):
\[
w = \frac{504}{84}
\]

4. Calculate \( \frac{504}{84} \):
\[
w = 6
\]

Thus, the width of the prism, rounded to the nearest foot, is:
\[
w = 6 \text{ ft}
\]