Derive the formula for Surface Area of Right Circular Cone.

Question

How is this related to volume of cone?

Answer 1

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.

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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.

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.

The base of a cone has radius is .

The height of the cone is .

The slant height of the cone is .

.

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 .

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

Length of the arc is .

Area of sector ABC is .

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

Substitute .

Surface area of the right circular cone is .

Step 3:

The volume of the cone is .

The relation between volume and surface area of a cone:

.

Solution:

Surface area of the right circular cone is .

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