Use the image to answer the question.
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.
What is the radius of the cone?
To find the radius of the cone, we can use the Pythagorean theorem. The slant height of the cone can be thought of as the hypotenuse of a right triangle, with the height and the radius as the other two sides.
Using the Pythagorean theorem, we have:
(radius)^2 + (height)^2 = (slant height)^2
Substituting the given values:
(radius)^2 + 12^2 = 10^2
Simplifying the equation:
(radius)^2 + 144 = 100
Subtracting 144 from both sides:
(radius)^2 = 100 - 144
(radius)^2 = -44
Since we cannot have a negative radius, it is not possible to determine the radius of the cone using the given information.