In a right circular cone, height, radius and slant height do not always be sides of a right triangle. Is the given statement true or false and justify your answer.
Solution:
Given, in a right circular cone, height, radius and slant height do not always be sides of a right triangle.
We have to determine if the given statement is true or false.
Consider a right circular cone with height h, slant height l and radius r.
In a right angled triangle one angle = 90°
∠AOB = 90°
Considering triangle AOB,
By using Pythagorean theorem
AB² = OA² + OB²
l² = h² + r²
This implies that the height, radius and slant height of the cone can always be the sides of a right triangle.
Therefore, the given statement is true.
✦ Try This: Find the volume of the right circular cone with radius 6 cm and height 7 cm.
Given, the radius of cone, r = 6 cm
Height of cone, h = 7 cm
We have to find the volume of cone
Volume of the cone = 1/3 πr²h
Where, r is the radius of the cone
h is the height of the cone
So, volume = 1/3 π(6)²(7)
= 1/3 π(36)(7)
= π(12)(7)
Therefore, volume = 84π cm³
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13
NCERT Exemplar Class 9 Maths Exercise 13.2 Problem 3
In a right circular cone, height, radius and slant height do not always be sides of a right triangle. Is the given statement true or false and justify your answer.
Summary:
The given statement “In a right circular cone, height, radius and slant height do not always be sides of a right triangle” is true
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