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Derive the formula for Surface Area of Right Circular Cone.

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How is this related to volume of cone?
asked Aug 17, 2015 in PRECALCULUS by anonymous

1 Answer

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A cone is a three-dimensional geometric figure.

A cone is a shape whose base is a circle and whose sides taper up to a point.

- See more at: http://www.uzinggo.com/observing-changes-surface-area-cones/volume-surface-area-cones-cylinders-spheres/algebra-foundations-grade-8#sthash.oGqWnp7j.dpuf

A cone is a three-dimensional geometric figure.

A cone is a shape whose base is a circle and whose sides taper up to a point.

- See more at: http://www.uzinggo.com/observing-changes-surface-area-cones/volume-surface-area-cones-cylinders-spheres/algebra-foundations-grade-8#sthash.oGqWnp7j.dpuf
A cone is a three-dimensional geometric figure.

Step 1:

The right circular cone is a three dimensional geometric figure.

A cone is a shape whose base is a circle and whose sides are taper up to a point.

image

The base of a cone has radius is image.

The height of the cone is image.

The slant height of the cone is image.

image

image.

Step 2:

The surface area of a cone is equal to the sum of the area of the base and the lateral area.

The area of the base is image.

The lateral area is equal to the area of the sector.

image

Length of the arc is image.

image

image

Area of sector ABC is image.

The surface area of a cone is equal to the sum of the area of the base and the lateral area.

image

image

Substitute image.

Surface area of the right circular cone is image.

Step 3:

The volume of the cone is image.

The relation between volume and surface area of a cone:

image

image

image.

Solution:

Surface area of the right circular cone is image.

The relation between volume and surface area of a cone is image.

answered Aug 17, 2015 by Sammi Mentor

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