Question
What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18cm?
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The base of the square pyramid must be a square with a side length of 18 cm, which means its area is 18 x 18 = 324 square cm.
The height of the pyramid can be found using the Pythagorean theorem:
h^2 = (18/2)^2 + (18/2)^2
h^2 = 9^2 + 9^2
h^2 = 162
h = √162 ≈ 12.73 cm
The volume of the pyramid is:
V = (1/3) x base area x height
V = (1/3) x 324 x 12.73
V ≈ 1,730.48 cubic cm
Therefore, the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm is approximately 1,730.48 cubic cm.
The height of the pyramid can be found using the Pythagorean theorem:
h^2 = (18/2)^2 + (18/2)^2
h^2 = 9^2 + 9^2
h^2 = 162
h = √162 ≈ 12.73 cm
The volume of the pyramid is:
V = (1/3) x base area x height
V = (1/3) x 324 x 12.73
V ≈ 1,730.48 cubic cm
Therefore, the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm is approximately 1,730.48 cubic cm.
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