What is the formula of a cylinder and sphere?

The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h.

Why is the volume of a sphere 2/3 the volume of a cylinder?

If the height of the cylinder equals the diameter of the sphere, , and if the diameter of the cylinder is equal to the diameter of the sphere, , so the volume is . This is half as much again as the volume of the sphere, which is two-thirds of the volume of the cylinder.

What is a sphere and cylinder?

These figures have curved surfaces, not flat faces. A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. The sphere is a space figure having all its points an equal distance from the center point.

What is volume of a cone to the volume of a sphere?

The areas shaded are all the same size (that is D=H). We know that volume of a cone is. Volume of cone = 13×πr2×h. Therefore volume of a sphere: (13×πr2×h)+(13×πr2×h)= ( 1 3 × π r 2 × h ) + ( 1 3 × π r 2 × h ) = Volume of a sphere.

What is the ratio of volume of cylinder and sphere?

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Why is the volume of a sphere 3 4?

Since the cylinder/cone and hemisphere have the same height, by Cavalieri’s Principle the volumes of the two are equal. The cylinder volume is πR3, the cone is a third that, so the hemisphere volume is 23πR3. Thus the sphere of radius R has volume 43πR3. Integration.

When was the volume of a sphere found?

287-212 B.C.
A spectacular landmark in the history of mathematics was the discovery by Archimedes (287-212 B.C.) that the volume of a solid sphere is two- thirds the volume of the smallest cylinder that surrounds it, and that the surface area of the sphere is also two-thirds the total surface area of the same cylinder.

How do you find the volume of cylinders and spheres?

1. The volume of a cone is linked to the volume of a cylinder. A cone is one third of the volume of a cylinder.
2. The volume of a sphere is ⁴/₃ × π × r³. To calculate the volume we multiply these values together.
3. The volume of a cylinder is π × r² × l (r is the radius of the circle and l is the length of the cylinder).

Why is the volume of a cylinder?

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, πr2h, where r is the radius of the circular base and h is the height of the cylinder.