Question

Find the volume of a pyramid with a square base, where the perimeter of the base is10.7 ft and the height of the pyramid is 9.8 ft. Round your answer to the nearesttenth of a cubic foot.

Answer 1

The volume of a pyramid is one third of the product between the base area and the height:

`V=(1)/(3)\cdot A_(base)\cdot h`

We already know the height of the pyramid, however we need to estimate the base area from the information given.

The base is a square. Squares have their four sides with the exat same length.

The perimeter is the sum of the length of the sides of a polygon, then, the perimeter of the square is four times its side:

`P=4\cdot L`

Where L is the length of the side. Now, knowing the perimeter we can estimate the lenght of the sides of the base, from which we can calculate the base area:

`\begin{gathered} 4\cdot L=P \\ L=(P)/(4) \\ L=(10.7ft)/(4) \\ L=2.675ft \end{gathered}`

Now we know the sides of the base have a length of 2.675 ft each. To estimate the area of the base we just need to square this lenght:

`A_{\text{base}}=L^2`

Then, to calculate the volume of the pyramid:

`\begin{gathered} V=(1)/(3)\cdot A_(base)\cdot h \\ \\ V=(1)/(3)\cdot L^2\cdot h \end{gathered}`

Let's replace values:

`\begin{gathered} V=(1)/(3)\cdot(2.675ft)^2\cdot9.8ft \\ V\approx23.375ft^3 \\ V\approx23.4ft^3 \end{gathered}`

The volume of the pyramid is approximately 23.4 cubic feet.