A rectangular pyramid has an area 24cm$^2$ and height 7.5cm. Find its volume?

Analysis

To find the volume of a pyramid, we need to use the standard geometric formula that relates the base area and the perpendicular height of the pyramid.

Concept

The volume ($V$) of any pyramid (whether rectangular, square, or triangular) is given by the formula:

This formula applies because a pyramid occupies exactly one-third of the volume of a prism with the same base and height.

Solution

Step 1: Identify the given values.

• Base Area ($A$) = $24 \text{ cm}^2$
• Height ($h$) = $7.5 \text{ cm}$

Step 2: Substitute the values into the formula.

Step 3: Perform the calculation. First, simplify the fraction:

Now, multiply $8$ by $7.5$:

So, $V = 60.0 \text{ cm}^3$.

Conclusion

Comparing our result to the given options, we find that the calculated volume matches option D.

Exam Tip

When dealing with volume problems for pyramids and cones, always remember the "one-third" rule. Students often forget to divide by 3 and end up calculating the volume of a prism instead. If you see "pyramid" or "cone," immediately write down $\frac{1}{3}$ to remind yourself!