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