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Showing content from http://www.mathsisfun.com/geometry/cone.html below:

Spinning Cone

Go to Surface Area or Volume.

Notice these interesting things:

• It has a circle at one end
• And a point at the other end
• And a curved side
• It is not a polyhedron as it has a curved surface

images/poly-gl.js?mode=cone

• The pointy end of a cone is called the apex
• The flat part is the base

An object shaped like a cone is said to be conical

This ice cream cone is

,

with spheres of ice cream on top

A cone can be made by rotating a right-angled triangle.

The triangle is rotated around either of its two shorter sides which becomes the axis of the cone.

A right cone has its apex directly above the center of its circular base:

An oblique cone has its apex offset from the center,
giving it a slanted appearance.

The Surface Area has two parts:

• The Base Area = π × r²
• The Side Area = π × r × s

Where r is the radius of the base, h is the cone's height and s is the slant length.

Which together makes:

Surface Area = π × r × (r + s)

The slant length can be calculated using Pythagoras:

s = √(r² + h²)

Surface Area of Base= π × r²

 = π × 2²

 = 4π

 â‰ˆ 12.57

Surface Area of Side= π × r × √(r²+h²)

 = π × 2 × √(2²+7²)

 = π × 2 × √(4+49)

 = 2π√(53)

 â‰ˆ 45.74

Total Surface Area ≈ 12.57 + 45.74 ≈ 58.31

Volume = 1 3 π × r² × h

Volume= 1 3 π × r² × h

 = 1 3 π × 2² × 7

 = 28 3 π

 â‰ˆ 29.32

Play with it here. The formula also works when it "leans over" (oblique) but remember that the height is always at right angles to the base:

images/geom-oblique-3d.js?mode=cone

The volume formulas for cones and cylinders are very similar:

So a cone's volume is exactly one third ( 1 3 ) of a cylinder's volume.

You should order your ice creams in cylinders, not cones, you get 3 times as much!

A cone is also like a pyramid with an infinite number of sides, see Pyramid vs Cone.

This is almost a cone, but the top is chopped off (called a "truncated cone").

Also it has a wider base added so it doesn't fall over!

873,874,875,876, 1833, 1834, 3399, 3400, 3401, 3402

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