Question
The cone below has a radius of 5 centimeters and a height of 12 centimeters.
Note: Figure is not drawn to scale.
The slant height of a cone is the distance along the curved surface of the cone from the base to the apex. What is the slant height of the cone shown above?
A.
13 centimeters
B.
10 centimeters
C.
17 centimeters
D.
16 centimeters
Note: Figure is not drawn to scale.
The slant height of a cone is the distance along the curved surface of the cone from the base to the apex. What is the slant height of the cone shown above?
A.
13 centimeters
B.
10 centimeters
C.
17 centimeters
D.
16 centimeters
Answers
GPT-4o mini
To find the slant height of the cone, we can use the Pythagorean theorem. The slant height \( l \) is the hypotenuse of a right triangle where one leg is the radius \( r \) of the base, and the other leg is the height \( h \) of the cone. The formula is given by:
\[
l = \sqrt{r^2 + h^2}
\]
In this case, the radius \( r = 5 \) cm and the height \( h = 12 \) cm. Plugging in these values:
\[
l = \sqrt{(5)^2 + (12)^2}
\]
\[
l = \sqrt{25 + 144}
\]
\[
l = \sqrt{169}
\]
\[
l = 13 \text{ cm}
\]
Therefore, the slant height of the cone is \( 13 \) centimeters.
The correct answer is **A. 13 centimeters**.
\[
l = \sqrt{r^2 + h^2}
\]
In this case, the radius \( r = 5 \) cm and the height \( h = 12 \) cm. Plugging in these values:
\[
l = \sqrt{(5)^2 + (12)^2}
\]
\[
l = \sqrt{25 + 144}
\]
\[
l = \sqrt{169}
\]
\[
l = 13 \text{ cm}
\]
Therefore, the slant height of the cone is \( 13 \) centimeters.
The correct answer is **A. 13 centimeters**.