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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