A cone is a solid created of a one and also its inner ( basic ), a given point not ~ above the aircraft of the one ( vertex ) and also all the segments from the suggest to the circle.

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The radius of the cone is the radius that the base.The altitude that the cone is the perpendicular segment indigenous the vertex to the plane of the base.The height that the cone is the size of the altitude. The axis the the cone is the segment whose endpoints are the vertex and the center of the base.If the axis is perpendicular come the airplane of the circle, the cone is a ideal cone otherwise it is an slope cone . The slant elevation of a best cone is the length of the segment from the peak of the cone come the circle of the base.Slant height is not identified for slope cones. A cone is closely related come a pyramid . So, the formulas for their surface ar areas and also volume are related.
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Remember, the formulas for the lateral surface ar area that a pyramid is 1 2 p together and also the total surface area is 1 2 ns together + B .

due to the fact that the base of a cone is a circle, us substitute 2 π r for ns and π r 2 because that B where r is the radius of the basic of the cone.

So, the formula for the lateral surface area the a ideal cone is L. S. A. = π r together , whereby l is the slant elevation of the cone.




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instance 1:

find the lateral surface ar area the a best cone if the radius is 4 cm and the slant height is 5 cm.

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l .S .A . = π ( 4 ) ( 5 )                               = 20 π                               ≈ 62.8 cm 2


The formula for the total surface area the a best cone is T .S .A . = π r l + π r 2 .


example 2:

discover the total surface area the a appropriate cone if the radius is 6 inches and also the slant elevation is 10 inches.

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T .S .A . = π ( 6 ) ( 10 ) + π ( 6 ) 2                               = 60 π + 36 π                               = 96 π in 2                               ≈ 301.59 in 2


because slant elevation is undefined for an slope cone, there room no formulas because that the areas of oblique cones. The volume of a circular cone is one-third the product the its altitude and also the area of its base. ( V = 1 3 B h ) .
example 3:

uncover the volume that a cone who altitude is 15 m and whose radius is 8 m.

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Therefore, the volume of the cone is around 1005.31 m 3 .


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