A cone shows a height marked as 12 and a diameter marked as 8, both indicated with perpendicular dotted lines. The slant height is marked as 10.

Answer 1

To find the slant height of a cone, we can use the Pythagorean Theorem.

Let's denote the radius of the cone as r, the height as h, and the slant height as l.

From the diagram, we can see that the slant height forms a right triangle with the height and the radius of the cone.

Using the Pythagorean Theorem, we have:

\( l^2 = r^2 + h^2 \)

Given that the diameter of the cone is 8, the radius would be half of that, so:

\( r = \frac{8}{2} = 4 \)

Given that the height is 12, and the slant height is 10, we can plug these values into the equation to solve for the slant height:

\( 10^2 = 4^2 + 12^2 \)

\( 100 = 16 + 144 \)

\( 100 = 160 \)

This equation is not true, so there might be an error in the given values or the calculation. Would you like to provide more information or correct any mistakes in the given data?