Question

The radius of a cone is 7 m and its height is 10 m. Then its slant height is______

• A. 12.2 m
• B. 13.5 m
• C. 14.5 m
• D. 16.2 m

Answer 1

The Correct Option is A

To solve the problem, we need to determine the slant height of a cone given its radius and height. The formula for the slant height (\( l \)) of a cone is derived from the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle with the radius (\( r \)) and the height (\( h \)) of the cone.

1. Formula for Slant Height:
The slant height \( l \) of a cone is given by:

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

where \( r \) is the radius and \( h \) is the height of the cone.

2. Substituting the Given Values:
We are given that the radius \( r = 7 \, \text{m} \) and the height \( h = 10 \, \text{m} \). Substitute these values into the formula:

\[ l = \sqrt{7^2 + 10^2} \]

Simplify the squares:

\[ l = \sqrt{49 + 100} \] \[ l = \sqrt{149} \]

3. Approximating the Square Root:
To find the approximate value of \( \sqrt{149} \), we can use a calculator or estimation methods. Using a calculator:

\[ \sqrt{149} \approx 12.2 \]

4. Final Answer:
The slant height of the cone is approximately \( 12.2 \, \text{m} \).

Final Answer:
The slant height is \( {12.2 \, \text{m}} \).