Formula to Figure Slant Height

Introduction about cone:

The slant height of a circular cone is the distance from any point on the circle to the apex of the cone. The slant height of a cone is given by the formula sqrt(r^2+h^2)  where r is the radius of the circle and h is the height from the center of the circle to the apex of the cone. If we know the value of radius and height of the circle, the slant height of cone can be finding using that formula. In this article we shall see how to calculate the slant of the cone .some example problems and practice problems. I like to share this Acute Angled Triangle with you all through my article.

(Source-Wikipedia)

Formula to Figure Slant Height of the Cone with Example Problems:

Slant height of the cone =  `sqrt (r^2+h^2) `

Where r - the radius of the circle

h - the height from the center of the circle to the apex of the cone

Problem 1:

Find the slant height of cone, which has the radius 6 cm and altitude14 cm.

Solution:

Given:

Radius (r) =6 cm.

Altitude (h) =14cm

Formula to figure slant height:

Slant height of the cone = `sqrt (r^2+h^2)` units

=`sqrt(6^2+14^2)`

=`sqrt(36 + 196)`

=`sqrt(232)`

= 15.23

Slant height of the cone = 15.23 cm

Problem 2:

Find the slant height of cone, which has the radius 7 cm and altitude15 cm .

Solution:

Given:

Radius (r) =7 cm.

Altitude (h) =15cm

Formula to figure slant height:

Slant height of the cone = `sqrt (r^2+h^2)`  units

=`sqrt(7^2+15^2)`

=`sqrt(49+ 225)`

=`sqrt(274)`

= 16.55

Slant height of the cone = 16.55 cm

Problem 3:

Find the slant height of cone, which has the radius 8 cm and altitude 16 cm.

Solution:

Given:

Radius (r) = 8 cm.

Altitude (h) =16 cm

Formula to figure slant height:

Slant height of the cone = `sqrt (r^2+h^2)` units

=`sqrt(8^2+16^2)`

=`sqrt(64+ 256)`

=`sqrt(320)`

=17.88

Slant height of the cone = 17.88 cm


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Practice Problems to Find the Slant Height:

1. Find the slant height of cone, which has the radius 9 m and altitude 17 m.

Answer: Slant height of the cone = 19.23 cm

2. Find the slant height of cone, which has the radius 10 cm and altitude 18 cm.

Answer: Slant height of the cone = 20.59 cm

3. Find the slant height of cone, which has the radius 11 m and altitude 19 cm.

Answer: Slant height of the cone = 21.954 cm