Question

In the adjoining figure, the slant height of the conical part is :

• A. 4 cm
• B. 7 cm
• C. 5 cm
• D. 25 cm

Hint:

The set (3, 4, 5) is a Pythagorean triple. If you see 3 and 4 as the legs of a right triangle, the hypotenuse (slant height) is always 5.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The slant height (\(l\)) of a cone is the distance from the apex to any point on the circumference of the base. It forms a right-angled triangle with the vertical height (\(h\)) and the radius (\(r\)).
Step 2: Key Formula or Approach:
Pythagoras' Theorem: \[ l = \sqrt{r^2 + h^2} \]
Step 3: Detailed Explanation:
Assuming the figure specifies a radius \(r = 3\) cm and a vertical height \(h = 4\) cm:
1. Substitute the values into the formula:
\[ l = \sqrt{3^2 + 4^2} \] 2. Calculate the squares:
\[ l = \sqrt{9 + 16} \] 3. Find the square root:
\[ l = \sqrt{25} = 5 \text{ cm} \]
Step 4: Final Answer:
The slant height of the conical part is 5 cm.