The height of the Pyramid with the base sides of 280m is 99.1875m.
Volume of the Pyramid
The volume of a pyramid is given as one-third of the product of the base area and height of the pyramid.
\(\rm{Volume\ of\ Pyramid= \dfrac{1}{3}\times (area\ of\ the\ base) \times (height\ of\ the\ pyramid)\)
Area of the square
The area of a square is the square of its side.
\(\rm{Area\ of\ Square= (side)^2\)
Given to us
- Great Pyramid of Cheops is a square-based pyramid,
- the base has sides of 230m,
- the height is 147m.
To find
- the height be if you give the base sides of 280m
Volume of the square Pyramid
As the base of the pyramid is a square therefore the volume of the pyramid can be written as
\(\rm{Volume\ of\ Pyramid= \dfrac{1}{3}\times (side\ of\ the\ base)^2 \times (height\ of\ the\ pyramid)\)
Height of the Pyramid
As we need to make the pyramid using the same material the volume of the pyramid will be constant, therefore, the same.
Volume of Great Pyramid of Cheops
= Volume of the pyramid with the base sides of 280m
\(\dfrac{1}{3}\times (230\ m)^2 \times (147\ m) = \dfrac{1}{3}\times (280\ m)^2 \times (h)\)
Canceling \(\dfrac{1}{3}\) from both sides,
\((230\ m)^2 \times (147\ m) = (280\ m)^2 \times (h)\\(280\ m)^2 \times (h) = (230\ m)^2 \times (147\ m) \\h=\dfrac{ (230\ m)^2 \times (147\ m) }{(280\ m)^2}\\h = 99.1875\ m\)
Hence, the height of the Pyramid with the base sides of 280m is 99.1875m.
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