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Question
In a right circular cone, height, radius and slant height do not always be sides of a right triangle.
Options
True
False
Solution
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.
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