Question

The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is:

• A. 24 cm
• B. 31 cm
• C. 26 cm
• D. 25 cm

Answer 1

The Correct Option is D

Objective:
Given the height (\(h\)) and radius (\(r\)) of a right circular cone, determine its slant height (\(l\)).
- Height (\(h\)) = 24 cm
- Radius (\(r\)) = 7 cm

Methodology:
1. Recognize that the height, radius, and slant height of a right circular cone form a right-angled triangle, with the slant height as the hypotenuse.
Apply the Pythagorean Theorem:
\[l^2 = r^2 + h^2\]
2. Substitute the given values into the formula:
\[l^2 = 7^2 + 24^2 = 49 + 576 = 625\]
Solve for \(l\):
\[l = \sqrt{625} = 25\]
Result:
The slant height of the cone is 25 cm.