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The Great Pyramid of Giza has a base that is 440 cubits by 440 cubits and is 280 cubits tall. Find the volume of the Great Pyramid.
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Volume of the great pyramid
mearing
The Great Pyramid of Giza
The area of the bottom of the pyramid is
440 \mbox{ cubits} * 440\mbox{ cubits} =193600\mbox{ cubits}^2
The scaling values of the top and bottom are:
s(0)=1
s(280)=0
This means that:
s(z)=1-\frac{z}{280}
The area formula is:
A(z)=193600(1-\frac{z}{280})^2
The volume of the Pyramid is:
\int_0^{280}193600(1-\frac{z}{280})^2dz=193600\int_0^{280}1-\frac{z}{140}+\frac{z^2}{78400}dz
=193600(z-\frac{z^2}{280}+\frac{z^3}{235200})\big|_0^{280}=18069333.3
\mbox{ cubits}^3
chowell1
The Great Pyramid
The area of the base is
440 \ \text{cubits} \ \times \ 440 \ \text{cubits} \ = 193600 \ \text{cubits}^2
Since the height is 280, the scaling values of the top and bottom are:
s(0) = 1\\
s(280) = 0
This means that the scaling factor is:
s(z) = 1 \ - \ \frac{z}{280}
With this, we can determine the area formula.
A(z) = 193600(1-\frac{z}{280})^2
Now, we can find the volume of the pyramid.
\int_0^{280}193600(1-\frac{z}{280})^2dz = 193600\int_0^{280}1 - \frac{z}{140} +\frac{z^2}{78400}dz \\\
=193600(z - \frac{z^2}{280} + \frac{z^3}{235200})|^{280}_0 = 18069333.3 \ \text{cubits}^3