Question

Find the height if the volume is 48 units 3 and the length of one side of the base is 4 units.

Answer 1

To find the height of a rectangular prism (or cuboid), we can use the formula for the volume:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

In this case, we are given:
- Volume = 48 cubic units
- One side of the base (which we can assume is the length) = 4 units

We need to determine the height. First, we need to establish the area of the base (assuming it's a square base for simplicity). If one side of the base is 4 units, then:

\[
\text{Area of the base} = \text{Length} \times \text{Width} = 4 \times 4 = 16 \text{ square units}
\]

However, since we are not specifically told that the base is square and we don't have the width, we'll assume a general length \( l = 4 \) and let \( w \) be the width. The formula for the volume then becomes:

\[
\text{Volume} = l \times w \times h = 4 \times w \times h
\]

Setting this equal to the given volume:

\[
48 = 4 \times w \times h
\]

Now, simplifying for \( w \times h \):

\[
4 \times w \times h = 48
\]
\[
w \times h = \frac{48}{4} = 12
\]

Now we have the equation \( w \times h = 12 \). Without the value of \( w \), we cannot determine a unique value for \( h \) because it can vary depending on \( w \). However, if we assume \( w = 4 \) (making the base a square), we can solve for \( h \):

If \( w = 4 \):
\[
4 \times h = 12 \implies h = \frac{12}{4} = 3
\]

Alternatively, if \( w \) takes on other values, \( h \) will adjust accordingly. For example, if \( w = 3 \), then:

\[
3 \times h = 12 \implies h = 4
\]

If \( w = 2 \):
\[
2 \times h = 12 \implies h = 6
\]

For generality, we can express \( h \) in terms of \( w \):

\[
h = \frac{12}{w}
\]

In conclusion, the height \( h \) can take multiple values depending on the width \( w \). If a specific \( w \) is provided, the height can be calculated directly.