Question

The Great Pyramid of Cheops is a square-based pyramid, the base has sides of 230m, and the height is 147m.
Using the same material, what would the height be if you give the base sides of 280m.

Please give the answer to the nearest metre.

Thank you :)

Please show full working out.

Answer 1

Hello,
If you mean by "using the same material" that all is scaled then
using Thales:

$\dfrac{280}{230} = \dfrac{h}{147} \\ ==\textgreater\ h= \dfrac{28*147}{23} =178.9565217....(m)$≈179 (m)

Answer 2

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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