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.