Question

the relation between l , r and h for a right circular cone is​

Answer 1

The relation between l, r, and h for a right circular cone is​ $l^{2} = r^{2} + h^{2}$.

Given:

l, r, and h

To Find:

The relation between l, r, and h for a right circular cone is​?

Solution:

When an axis of a cone is perpendicular to or makes a right angle with the base, then that type of cone is called a right circular cone.

A right circular cone has height h, slant height l, a base with radius r, and a vertex.

The relation between slant height l, radius r, and height h can be derived by using the Pythagoras theorem as it forms a right-angled triangle.

According to the Pythagorean theorem,

$(Hypotenuse)^{2} = (Base)^{2} + (Height)^{2}$ ----------------- (1)

For the right circular cone,

Hypotenuse = slant height l,

Base = radius r, and

Height = h

Putting the values in equation (1), we get

$l^{2} =r^{2} +h^{2}$

or $l =}\sqrt{r^{2} +h^{2}$

Hence, the relation between l, r, and h for a right circular cone is​ $l^{2} = r^{2} + h^{2}$.

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