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In Geometry, an object having width, height and depth is referred to as a 3D solid object. A cone is a solid that has a circular base and a single vertex.

Types of Cones

Cones can be either right cones or oblique cones.

If the vertex is exactly over the center of the base of the cone then it is known as a right cone.

If the vertex is not over the center of the base of the cone, then it is known as an oblique cone.

                                                         

Volume of a cone

The volume of a cone is defined as the number of cubic units that will exactly fill the cone.

If r is the radius of the circular base of the cone and h is the height of the cone, then the volume of the cone is given by the formula

Volume = ⅓  π r2 h

The volume is expressed in cubic units.

Practice questions:
Question: Find the volume of a cone with radius equal to 3 cms and height equal to 7 cms.
( Answer:    Radius of the cone r = 3 cms
        Height of the cone h = 7 cms
        π = 22 / 7
        Volume of the cone     = ⅓ * 22/ 7 * 3 * 3 * 7
                    = 66 cubic cms
)

Question: Find the volume of a cone with radius equal to 1 cms and height equal to 21 cms.
( Answer:  22 cubic cms )

Area of the cone

The surface area of a cone is calculated as the sum of the surface area of the curved surface of the cone and the surface area of the circular base of the cone.

If r is the radius of the cone, and s is the slant of the cone, then the area of the cone is given by the formula = π r s + π r2

The area of the cone is measured in sq cms.

Practice questions:
Question: Find the surface area of a cone with radius equal to 7 cms and slant equal to 14 cms.
( Answer:    Radius of the cone r = 7 cms
Slant of the cone s = 14 cms
Area of the cone     = 22/7 * 7 * 14 + 22/7 * 7 * 7
=  308 + 154
= 462 sq cms    
)

Question: Find the surface area of a cone whose circular base has a diameter of 14 cms and its slant is equal to 10 cms.
( Answer:     Diameter of the circular base = 14 cms
        Radius of the cone r = 14/2 = 7 cms
        Slant of the cone = 10 cms
        Area of the cone     = 22/7 * 7 * 10 + 22/7 * 7 * 7
                    = 220 + 154
                    = 374 sq cms
)

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