A cylinder is inscribed in a cube. If the edge of the cube is 3" long, find the volume of the cylinder.

the answer is 27/4 pi inches 3

Actually, you don't have to multiply by pie. I take the same course as this anonymous person and I got 100 on my assignment. You just multiply 2.25 times the 3 and you have your answer :)

pi* sorry for the misspell :) I'm hungry so pie sounds yummier doesn't it? anyways, good luck with your geometry :)

To find the volume of the cylinder, we need to know its height and radius. Since the cylinder is inscribed in a cube, its height will be equal to the edge length of the cube.

Given that the edge of the cube is 3", the height of the cylinder will also be 3".

To find the radius of the cylinder, we need to consider the relationship between the radius and the edge length of the cube. The diagonal of a face of the cube is equal to the diameter of the inscribed cylinder. By using the Pythagorean theorem, we can calculate the diagonal:

Diagonal^2 = Edge^2 + Edge^2
Diagonal^2 = 3^2 + 3^2
Diagonal^2 = 9 + 9
Diagonal^2 = 18

To find the radius, we divide the diagonal by 2 (since the diagonal is equal to the diameter):

Radius = Diagonal / 2
Radius = √18 / 2
Radius = √9 * √2 / 2
Radius = 3√2 / 2

Now we have the height of the cylinder (3") and the radius (√2/2 * 3"). To calculate the volume of the cylinder, we will use the formula:

Volume = π * radius^2 * height

Substituting the values we found:

Volume = π * (3√2 / 2)^2 * 3
Volume = π * (9 * 2 / 4) * 3
Volume = π * (18 / 4) * 3
Volume = π * 4.5 * 3
Volume = 13.5π square inches

Therefore, the volume of the cylinder is approximately 42.41 cubic inches.

The diameter must also be 3 inches.

V = pi * r^2 * h

V = 3.14 * 1.5^2 * 3
V = 3.14 * 2.25 * 3
V = ? cubic inches

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