To identify the radius of the cone as given in the problem, we start by noting that the radius is already provided: 5 centimeters. However, if needed, let’s clarify how these measurements relate to the cone's geometry.
Given:
- Height (h) of the cone = 12 cm
- Radius (r) of the cone = 5 cm
Formulae:
- Volume of a Cone: \( V = \frac{1}{3} \pi r^2 h \)
- Surface Area of the Cone:
- Lateral Area: \( A_L = \pi r l \) (where \( l \) is the slant height)
- Base Area: \( A_B = \pi r^2 \)
- Total Surface Area: \( A = A_L + A_B = \pi r l + \pi r^2 \)
Slant Height Calculation:
The slant height \( l \) of a cone can be found using the Pythagorean theorem, considering the radius and height as the two shorter sides of a right triangle, with the slant height being the hypotenuse:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the values we have:
\[ l = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ cm} \]
Summary:
- The radius of the cone is already provided as 5 centimeters.
- The calculated slant height is 13 centimeters.
If you need any further information or other specific calculations related to the cone, please let me know!