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What dimensions do you need for a cylinder to have the same volume as a sphere with a radius of 7?
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)
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What are dimensions of volume of a sphere and volume of a cylinder?
x^3
How can you prove that the volume of a sphere is equal to the volume of a cylinder provided their radii are equal and the height of the cylinder is equal to the diameter of the sphere?
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.
Is the volume of a sphere with a radius of r inches always equal to the volume of a cylinder with a radius of r inches?
No, it rarely is.
What is the volume of a circular cylinder whose height is 40m and whose radius is 20m Find the volume of a sphere whose radius is 20m?
the cylinder is approximately 50240 m3 the sphere is approximately 33493 and 1/3 m3
How does the volume change if the radius is tripled?
It depends on the shape. The volume of a sphere will increase differently to the volume of a cylinder, for example.
What is the relationship between the volume formula for a sphere and the volume formula for a cylinder?
-- 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 the largest possible right circular cylinder that can be inscribed in a sphere of radius a?
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
What is the formula for volume of a radius?
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.
What is the volume of a cylinder with the following dimensions of 6 ftt radius 24 ft height?
A cylinder with a radius of 6 feet and a height of 24 feet has a volume of 2,714.34 cubic feet.
What is the volume of a cylinder with ends that are half spheres with a radius of 4 and has a height of 12?
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)
Why are there two different formulas for calculating a cylinder and a sphere?
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.
What is the volume of a sphere with a radius of 4 centimeters?
The volume of a sphere with a radius of 4cm is about 268cm3
