Question

In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

On rotating a right-angled triangle AOB about OA, it generates a cone. The point A is the vertex of a cone. Its base is a circle with centre O and radius OB. The length OA is the height of the cone and the length AB is called its slant height.

Clearly, ∠AOB = 90°

Let the radius of the base be r units, height = h units and slant height = l units, then

`l^2 = h^2 + r^2 \implies l = sqrt(h^2 + r^2)`

Hence, in right circular cone, height, radius and slant height always be sides of a right triangle.