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

Problem:
We are given the height and radius of a right circular cone:
- Height (\(h\)) = 24 cm
- Radius (\(r\)) = 7 cm
We are asked to find the slant height (\(l\)) of the cone.

Step 1: Understand the geometry of a right circular cone
A right circular cone forms a right-angled triangle with the height as one leg, the radius as the other leg, and the slant height as the hypotenuse.
So we can apply the Pythagoras Theorem:
\[ l^2 = r^2 + h^2 \]

Step 2: Substitute the known values into the formula
\[ l^2 = 7^2 + 24^2 = 49 + 576 = 625 \Rightarrow l = \sqrt{625} = 25 \]

Final Answer:
The slant height of the cone is 25 cm.