# The Formula for the Length of a Painter's Line on a Cone

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## The Formula for the Length of a Painter's Line on a Cone

The length of the cone painter's line is

s = √(r² + t²)

### Detailed discussion of Cones

Cone is form pyramid with a circular base. If the apex of the cone is directly above the center of the circle, then the cone is called a perpendicular cone. If the apex of the cone is not directly above the center of the circle, then the cone is called an oblique cone.

The shaded side is called the base of the cone.

Point O is called the center of the circle (or center of the base of the cone) and point C is called the apex of the cone.

The line segment OA is called the radius of the base of the cone.

The line AB is called the diameter of the base of the cone.

The line segment connecting points C and O is called the height of the cone (t).

The line segment AD is called the chord of the base of the cone.

The side that is not shaded is called the conic blanket.

The line segments on the conic blanket that connect the vertex C and the points on the circle (eg AC) are called conic painter lines (s).

#### Where r is the radius of the base of the cone and t is the height of the cone.

The area of the cone blanket is π . r . s,

where r is the radius of the base of the cone, s is the length of the contour of the cone, and π = 3.14 or 22/7.

The area of the base of the cone or the area of the circle is

L = π . r²

where r is the radius of the base of the cone and π = 3.14 or 22/7.

Cone Surface Area

L = area of the cone blanket + area of the base of the cone

⇔ L = π . r . s + π . r²

⇔ L = π . r . (s + r)

where r is the radius of the base of the cone, s is the painter line of the cone, and π = 3.14 or 22/7.

Cone Volume

V = 1/3 . (area of base of cone . height of cone)

⇔ V = 1/3 . π . r² . t

where r is the radius of the base of the cone, t is the height of the cone, and π = 3.14 or 22/7.

Question Details

Class : IX (3 SMP)

Material: Build Space

Keywords: cone, length, line, painter

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