Question

Help me find the volume of this shape. It is a square pyramid.

Answer 1

Given the square pyramid shown in the picture, you need to use the following formula for calculating the volume of a square pyramid:

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

Where "a" is the length of an edge of the base, and "h" is the height of the pyramid.

Notice that the exercise does not provide the height, but you can find it using this Right Triangle formed in the pyramid:

And applying the Pythagorean Theorem, which states that:

`C^2=A^2+B^2`

Where "C" is the hypotenuse of the Right Triangle, and "A" and "B" are the legs.

In this case:

`\begin{gathered} C=5 \\ A=h \\ B=3 \end{gathered}`

Therefore, by substituting values and solving for "h", you get:

`\begin{gathered} 5^2=h^2+3^2 \\ √(25-9)=h \\ h=4units \end{gathered}`

Knowing the height, you can substitute all the values into the formula and calculate the volume of the pyramid:

`V=((6units)^2(4units))/(3)`
`V=48units^3`

Hence, the answer is:

`V=48units^3`