To determine the height of a pyramid given the area of the base and the volume, we can use the formula for the volume of a pyramid. The volume \(\(V\)\) of a pyramid is given by the formula:
\(\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]\)
Here, we are provided with:
- The area of the base \(\( \text{base area} = 24 \, \text{square inches} \)\)
- The volume \(\( V = 48 \, \text{cubic inches} \)\)
Given these values, we need to find the height \(\( h \)\). Let's rearrange the volume formula to solve for height. First, we isolate \(\( h \)\) on one side of the equation:
\(\[ V = \frac{1}{3} \times \text{base area} \times h \]\)
Multiply both sides by 3 to get rid of the fraction:
\(\[ 3V = \text{base area} \times h \]\)
Now, divide both sides by the base area to solve for \(\( h \)\):
\(\[ h = \frac{3V}{\text{base area}} \]\)
Substitute in the given values for \(\( V \)\) and the base area:
\(\[ h = \frac{3 \times 48}{24} \]\)
\(\[ h = \frac{144}{24} \]\)
\(\[ h = 6 \]\)
Therefore, the height of the pyramid is 6 inches.
