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: Problem Identification: A right circular cone is defined by a height of 24 cm and a radius of 7 cm. The objective is to determine its slant height.

Step 2: Application of the Pythagorean Theorem: Within a right circular cone, the radius \( r \), height \( h \), and slant height \( l \) form a right triangle, with the slant height serving as the hypotenuse. The Pythagorean theorem applies as follows: \[l^2 = r^2 + h^2\] where: - \( l \) represents the slant height, - \( r = 7 \) cm denotes the radius, - \( h = 24 \) cm indicates the height.

Step 3: Value Substitution and Calculation: Substitute the given values of \( r = 7 \) cm and \( h = 24 \) cm into the equation: \[l^2 = 7^2 + 24^2\] \[l^2 = 49 + 576\] \[l^2 = 625\] Calculate \( l \) by taking the square root of both sides: \[l = \sqrt{625} = 25 \text{ cm}\]

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