A largest possible cylinder is inscribed within a cube. What portion of the cube would be occupied by the cylinder?
Answers
What is the volume of the largest cylinder that can be cut from a cube having area equal to 600m^2?
Cube has 6 faces.
If area is 600 m², area of each face would be 600/6 = 100m²
=> Each edge of cube = √100 = 10m.
Maximum diameter & maximum height of required cylinder cannot exceed the length of edge of the cube.
=> Radius of cylinder = 10/2 = 5m & height = 10m.
Volume of cylinder = πr²h
= 22/7 x 5 x 5 x 10 = 785.71 m²
:-)
So a cube has six faces. If the total area is 600 m^2, then each face is 100 m^2 or 10 m on a side.
In a cube, the largest inscribed cylinder is the height of the cube with radius 1/2 the cube’s dimension. So for the 10 m cube, it’s 10 m high and 5 m radius for a volume of pi*5^2*10 = 250 pi cubic meters, about 785.4 m^3.
It’s not entirely clear from your statement of the problem whether 600 m² is the total surface area of the cube or the area of one face of the cube.
In either case the volume of the largest cylinder is equal to π(s3)4 where s equals the edge length of the cube.
Therefore, in the first case (600m² = total surface area of the cube) the largest cylinder would have a volume of 785.40 m³, while in the second case (600 m² = area of one face of the cube) the largest cylinder would have a volume of 11,542.95 m³.
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