Question

The great pyramid outside cairo, Egypt has a square base measuring 756 feet on a side and a height of 480 feet. what is the volume of the great pyramid in cubic yards?

Answer 1

Answer:

The volume of the pyramid in cubic yards is

$3,386,880\ yd^{3}$

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

$V=\frac{1}{3}Bh$

whereB is the area of the base of the pyramid

h is the height of the pyramid

Step 1

Convert feet to yards

Remember that

$1 ft=\frac{1}{3}yd$

$756\ ft=756*\frac{1}{3}=252\ yd$ -----> square base measure

$480\ ft=480*\frac{1}{3}=160\ yd$ -----> height measure

Step 2

Find the volume of the pyramid

Find the area of the base B

$B=252^{2}=63,504\ yd^{2}$

substitute the values of B and h in the formula

$V=\frac{1}{3}(63,504)(160)=3,386,880\ yd^{3}$

Answer 2

First thing that needs to be done is to calculate for the area of the base which is in form of a square. The area is square is calculated through the equation,
                    A = s²
where A is area and s is the length of the sides.

Substituting the known values,
                   A = (756 ft)²
                  A = 571,536 ft²

The prism in which this pyramid can be enclosed has a volume that can be calculated through the equation.
          Volume = area of base x height
Substituting,
        Volume = (571,536 ft²)(480 ft)
         Volume = 274337280 ft³

The volume of the pyramid is equal to one-third (1/3) of the volume of the prism. Thus,
     Volume of pyramid = (274337280 ft³) / 3
     Volume of pyramid = 91445760 ft³

Thus, the volume of the pyramid is equal to 91,445,760 ft³.