The size of the space occupied by a cone is called its volume.

The volume of a cone is equal to 65438+ 0/3 of the volume of a cylinder with equal bottom and equal height.

According to the cylinder volume formula (v = sh = π r 2 * h), the cone volume formula is obtained:

Where s is the area of the bottom, h is the height and r is the radius of the bottom.

Extended data

Proof of volume formula

The cone can be regarded as a right-angled triangle with a height of H and a base of R, and rotates around the edge with a height of H, so the triangle relationship is established in the right-angled coordinate system, and the equation of its hypotenuse is

A cone is made up of straight lines.

,

The volume of the rotator obtained by rotating the triangle surrounded by the X axis around the X axis is:

computing formula

The side area of the cone = the square of the bus ××π× (the degree of the 360th sector).

The side area of the cone = 1/2× bus length× bottom circumference.

Lateral area of cone = π× radius of bottom circle× generatrix.

Surface area of cone = bottom area+side area S=πr? +πrl (note l= bus)

The volume of the cone = 1/3 the bottom area times the height or1/3 π r 2 * h.

References:

Baidu encyclopedia-cone