Question

7. Find the volume of the square pyramid given the slant height of 13 ft.4pts13 ft10 ft10 ft

Answer 1

400 ft³

Step-by-step explanation:

The volume of a square pyramid can be calculated as:

`V=(1)/(3)a^2h`

Where a is the side of the square and h is the height of the pyramid.

Now, we need to calculate the height using the slant height, so we will use the following equation:

`h=\sqrt[]{s^2-(a^2)/(4)}`

So, the height of the pyramid is equal to:

`\begin{gathered} h=\sqrt[]{13^2-(10^2)/(4)} \\ h=\sqrt[]{169-(100)/(4)} \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144} \\ h=12 \end{gathered}`

Then, the volume of the square pyramid is equal to:

`\begin{gathered} V=(1)/(3)(10)^2(12) \\ V=(1)/(3)(100)(12) \\ V=400 \end{gathered}`

Therefore, the answer is 400 ft³