To find the height of a pyramid given its volume and base area, we can use the formula for the volume of a pyramid:
[tex]\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\][/tex]
Given:
- [tex]\( V = 600 \, \text{cm}^3 \)[/tex]
- [tex]\(\text{base area} = 24 \, \text{cm}^2 \)[/tex]
We need to find the height of the pyramid ([tex]\(h\)[/tex]).
Step 1: Write the formula for the volume of the pyramid.
[tex]\[
600 = \frac{1}{3} \times 24 \times h
\][/tex]
Step 2: Simplify the equation.
[tex]\[
600 = 8h
\][/tex]
Step 3: Solve for [tex]\(h\)[/tex] by dividing both sides of the equation by 8.
[tex]\[
h = \frac{600}{8}
\][/tex]
Step 4: Calculate the division.
[tex]\[
h = 75
\][/tex]
So, the height of the pyramid is:
[tex]\[
\boxed{75} \, \text{cm}
\][/tex]
