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:
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.
The cone development diagram consists of a sector (the side of the cone) and a circle (the bottom of the cone).
When drawing the development diagram of a specified cone, a (bus length) and d (base diameter) are generally known.
∫ The circumference of an arc AB=⊙O O o.
∴ arc AB=πd
∫ arc AB = 2πa(≈ 1/360)
∴2πa(∠ 1/360 )=πd
∴2a(∠ 1/360 )=d
Bring a and d into 2a(≈ 1/360)= d to get the value of ∠ 1. In this way, all the data needed to draw the expansion diagram are obtained. According to the data, we can draw the expansion diagram of the cone.
A cone whose generatrix length is equal to the diameter of the bottom circle is a semicircle. The sector angles of all cones are equal to (base diameter ÷ generatrix) × 180 degrees.
References:
Baidu encyclopedia-cone