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

Step 1: Understanding the problem:
We are given a right circular cone with a height of 24 cm and a radius of 7 cm. We need to find the slant height of the cone.

Step 2: Using the Pythagorean theorem:
In a right circular cone, the radius \( r \), the height \( h \), and the slant height \( l \) form a right triangle, where the slant height is the hypotenuse. The Pythagorean theorem can be applied to this right triangle:
\[ l^2 = r^2 + h^2 \] where:
- \( l \) is the slant height,
- \( r = 7 \) cm is the radius,
- \( h = 24 \) cm is the height.

Step 3: Substituting the known values:
Substitute \( r = 7 \) cm and \( h = 24 \) cm into the equation:
\[ l^2 = 7^2 + 24^2 \] \[ l^2 = 49 + 576 \] \[ l^2 = 625 \] Now, take the square root of both sides to find \( l \):
\[ l = \sqrt{625} = 25 \text{ cm} \]

Step 4: Conclusion:
The slant height of the cone is \( 25 \) cm.