Question

Find the volume of material used to
construct the Red Pyramid in Cairo,
given that it has a height of 105 m, a
base length of 220 m, and is estimated
to be 96% solid.​

Answer 1

Given:

The material used to  construct the Red Pyramid in Cairo,  given that it has a height of 105 m, a base length of 220 m, and is estimated  to be 96% solid.​

To find:

The volume of material used to  construct the Red Pyramid in Cairo

Solution:

The height of the Red Pyramid, h = 105 m

The base length of the Red Pyramid, b = 220 m

The percentage of the solid material used = 96%

Here the Red Pyramid is a square-based pyramid, so the formula to find the volume of the square-based pyramid is as follows:

$\boxed{\bold{Volume \:of \:a\:square\: pyramid= \frac{1}{3} \times (Area \:of \:base) \times Height}}$

Now, substituting the given values in the formula above, we get

The volume of the material used to construct the Red Pyramid is,

= 96% of [The volume of a square pyramid]

= 96% × [$\frac{1}{3} \times (b)^2 \times h$]

= $\frac{96}{100} \times \frac{1}{3} \times (220)^2 \times 105$

= $0.96 \times \frac{1}{3} \times 48400 \times 105$

= $0.96 \times 48400 \times 35$

= $\bold{1626240\:m^3}$

Thus, the volume of material used to construct the Red pyramid in Cairo is 1626240 m³.

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