Question

If the height of a conical tent is 3 m and the radius of its base is 4 m, then the slant height of the tent is

• A. 3 m
• B. 4 m
• C. 5 m
• D. 7 m

Answer 1

The Correct Option is C

Given: A conical tent with:

• Height (\( h \)) = 3 m
• Radius of base (\( r \)) = 4 m

Step 1: Use the Pythagorean Theorem 

In a right-angled triangle formed by the radius, height, and slant height (\( l \)):

\[ l^2 = r^2 + h^2 \] \[ l^2 = 4^2 + 3^2 = 16 + 9 = 25 \] \[ l = \sqrt{25} = 5 \text{ m} \]

Final Answer: 5 m

Answer 2

To find the slant height of a conical tent, we can use the Pythagorean theorem. A cone's slant height (\( l \)) can be determined by the relationship between its height (\( h \)) and the radius of its base (\( r \)).

Given:

• Height (\( h \)) = 3 m
• Radius (\( r \)) = 4 m

The formula for the slant height (\( l \)) of a cone is:

\[ l = \sqrt{h^2 + r^2} \]

Substitute the given values:

\[ l = \sqrt{3^2 + 4^2} \]

\[ l = \sqrt{9 + 16} \]

\[ l = \sqrt{25} \]

\[ l = 5 \, \text{m} \]

Thus, the slant height of the tent is 5 m.