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Volume sphere = 4/3 πr³ = 4/3 π 7³ = 1372π/3

Volume cylinder = πr²h = 1372π/3

→ r²h = 1372/3

So as long as the radius of the cylinder is related to its height by:

radius = √(1372 / (3×height))

or

height = 1372 / (3×radius²)

You can have a cylinder of almost any size you want.

Example sizes:

radius 1, height 1372/3

radius 7, height 28/3

height 7, radius 14/√3

height 28/3, radius 7

height 49, radius √(28/3)

Q: What dimensions do you need for a cylinder to have the same volume as a sphere with a radius of 7?

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I'm quite sure this is impossible to prove, because the volume of a sphere is not equal to the volume of a cylinder with the same radius and height equal to the sphere's diameter. This can be shown as: Volume of sphere = (4*pi*r3) / 3. Volume of cylinder = pi*r2*h. Here, the height, h, of the cylinder = d = 2r. So, the volume of the cylinder = pi*r2*2r = 2*pi*r3, which obviously does not equal the volume of the sphere. The volume of half a sphere (with radius r) is equal to the volume of a cylinder(whose height is equal to its radius, r) minus the volume of a cone with the same height and radius. Therefore, the volume of a sphere is just double that. If you follow the nearby link, you can see a nice demonstration of that.

No, it rarely is.

the cylinder is approximately 50240 m3 the sphere is approximately 33493 and 1/3 m3

It depends on the shape. The volume of a sphere will increase differently to the volume of a cylinder, for example.

-- Volume of a sphere = 4/3 x (pi) x (radius)3 -- Volume of a cylinder = (pi) x (radius)2 x (length) The only relationship I can see is that they both involve (pi).

volume of a regular right circular cylinder is V=pi(r2)h since the radius is (a) then the height of the circular cylinder would be (2a) so the volume of the largest possible right circular cylinder is... V=2(pi)(r2)(a) with (pi) being 3.14159 with (r) being the radius of the circle on the top and bottom of the cylinder with (a) being the radius of the sphere

A radius is the distance from the centre of a circle (or sphere) to its circumference (or surface). It is a straight line and has dimensions [L]. It has only a length, no volume. So there is no such furmula.

A cylinder with a radius of 6 feet and a height of 24 feet has a volume of 2,714.34 cubic feet.

Each half-sphere occupies a height of 4. Effectively, there is a full sphere of radius 4 and a cylinder of length 4. The volume of the sphere = 4/3πr³ = 4/3π4³ = 268.08 The volume of the cylinder = πr²h = π4² x 4 = 201.06 Total volume = 268.08 + 201.06 = 469.14 (2dp)

Cylinders and spheres are different geometric shapes with different properties. The formulas for calculating their volume and surface area reflect these differences in shape and dimensions. The formula for a cylinder involves multiplying the base area by the height, while the formula for a sphere involves powers of the radius to account for its spherical shape.

The volume of a sphere with a radius of 4cm is about 268cm3