# CONOID

Definition of Conoid:

This is a solid which is also known as cone that is generated by rotating a line segment which is passing through a fixed point and making a constant angle with a fixed line. In the above figure of right circular cone, here , VO is a fixed line and VA is a rotating line which is making constant angle with VO.The point A would describe a circle with center O such that the line segment VO is perpendicular to the base.

VO is the height "h" and OA is the base radius "r" of the right circular cone VA is the slant height "l" of the right circular cone

It is very clear VAO is right angled triangle and the right angle is at at O.

Since VAO is the right angled triangle by Pythagorean theorem

we have l² = h² + r²

from l² = h² + r² , we can get the value of one of the measurements if we know the value of the other two measurements. For example, if we have the height "h", and the radius "r" of the right circular cone, we can easily determine the value of the slant height "l" of the right circular cone.

## Conoid-Example

Example:

If the height and radius of a right circular cone are 4cm and 3cm respectively,find the slant height of the conoid.

Solution:

Let us plug the known values in to the equation.

l² = h² + r²

l² = 4² + 3²

l² = 16 + 9

l² = 25

so l = 5

that is slant height = 5 cm

Role of radius,slant height and height in finding area and volume:

Measurement of radius,height and slant height plays a vital role in finding curved surface area, total surface area and volumes.

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Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 