To determine the length of a cone, which is commonly referred to as the slant height, we can use the Pythagorean theorem. In the case of a cone, the slant height (l) can be found using the formula:
\[ l = \sqrt{r^2 + h^2} \]
where \( r \) is the radius of the base and \( h \) is the height of the cone.
From your description:
- The height (h) of the cone is 4 cm (top to bottom)
- The diameter is 2 cm (side to side), which means the radius (r) is half of the diameter: \( r = \frac{2}{2} = 1 , \text{cm} \)
Now, substituting these values into the formula:
\[ l = \sqrt{(1, \text{cm})^2 + (4, \text{cm})^2} \] \[ l = \sqrt{1 + 16} \] \[ l = \sqrt{17} \] \[ l \approx 4.12, \text{cm} \]
Thus, the length (slant height) of the cone is approximately:
4.12 cm.