Volume of a Square Pyramid – Formulas and Examples

We have the following lengths

• Sides of the square, $latex l=4$
• Height of pyramid, $latex h=5$

Therefore, we use these values in the volume formula:

$latex V=\frac{1}{3}{{l}^2}\times h$

$latex V=\frac{1}{3}{{(4)}^2}\times (5)$

$latex V=\frac{1}{3}(16)\times (5)$

$latex V=26.67$

The volume is equal to 26.67 m³.

From the question, we get the following information:

• Sides of the square, $latex l=5$
• Height of pyramid, $latex h=6$

By substituting these values into the volume formula, we have:

$latex V=\frac{1}{3}{{l}^2}\times h$

$latex V=\frac{1}{3}{{(5)}^2}\times (6)$

$latex V=\frac{1}{3}(25)\times (6)$

$latex V=50$

The volume is equal to 50 m³.

We observe the following information:

• Sides of the square, $latex l=8$
• Height of pyramid, $latex h=9$

Using these values in the volume formula, we have:

$latex V=\frac{1}{3}{{l}^2}\times h$

$latex V=\frac{1}{3}{{(8)}^2}\times (9)$

$latex V=\frac{1}{3}(64)\times (9)$

$latex V=192$

The volume is equal to 192 m³.

We have the following values:

• Sides of the square, $latex l=6$
• Volume, $latex V=96$

In this case, we have the volume and we want to find the length of the height of the pyramid. Therefore, we use the volume formula and solve for h:

$latex V=\frac{1}{3}{{l}^2}\times h$

$latex 96=\frac{1}{3}{{(6)}^2}\times h$

$latex 96=\frac{1}{3}(36)\times h$

$latex 96=12 h$

$latex h=8$

The length of the height is equal to 8 m.

We have the following information:

• Height, $latex h=9$
• Volume, $latex V=75$

We use the volume formula and solve for it:

$latex V=\frac{1}{3}{{l}^2}\times h$

$latex 75=\frac{1}{3}{{l}^2}\times (9)$

$latex 75=3{{l}^2}$

$latex {{l}^2}=25$

$latex l=5$

The length of the sides is equal to 5 m.