Question

If radius of cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ...................... .

• A. 17 cm
• B. 4 cm
• C. 13 cm
• D. 60 cm

Hint:

This problem uses the (5, 12, 13) Pythagorean triplet. Being familiar with this triplet allows for immediate identification of the answer. When you see a radius and height of 5 and 12 (or vice versa) in a cone or pyramid problem, the slant height will almost certainly be 13.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In a right circular cone, the radius (\(r\)), the perpendicular height (\(h\)), and the slant height (\(l\)) form a right-angled triangle. The slant height (\(l\)) is the hypotenuse of this triangle.

Step 2: Key Formula or Approach:
We can use the Pythagorean theorem to relate the radius, height, and slant height of the cone:
\[ l^2 = r^2 + h^2 \] Taking the square root gives the formula for the slant height:
\[ l = \sqrt{r^2 + h^2} \]

Step 3: Detailed Explanation:
We are given the following values:
Radius, \(r = 5\) cm
Perpendicular height, \(h = 12\) cm
Substitute these values into the formula for slant height:
\[ l = \sqrt{5^2 + 12^2} \] \[ l = \sqrt{25 + 144} \] \[ l = \sqrt{169} \] \[ l = 13 \] So, the slant height is 13 cm.

Step 4: Final Answer:
The slant height of the cone is 13 cm.