Question

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

Answer 1

Answer:

400 ft³

Explanation:

The volume of a square pyramid can be calculated as:

$V=\frac{1}{3}a^2h$

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:

$h=\sqrt[]{s^2-\frac{a^2}{4}}$

So, the height of the pyramid is equal to:

$\begin{gathered} h=\sqrt[]{13^2-\frac{10^2}{4}} \\ h=\sqrt[]{169-\frac{100}{4}} \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144} \\ h=12 \end{gathered}$

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

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

Therefore, the answer is 400 ft³