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?
Responses
4
4 - not selected, this is the correct answer
10
10 - no response given
8
8 - incorrect
12
8
no
I apologize for the confusion. The correct answer is 4.
explain
I apologize for the incorrect response earlier. To find the radius of the cone, we can use the Pythagorean theorem.
The slant height of the cone (10) represents the hypotenuse of a right triangle. The height (12) and the radius (which we want to find) represent the other two sides of the triangle.
Using the Pythagorean theorem, we have the equation:
(radius)^2 + (height)^2 = (slant height)^2
We can substitute the given values into the equation:
(radius)^2 + (12)^2 = (10)^2
(radius)^2 + 144 = 100
(radius)^2 = 100 - 144
(radius)^2 = -44 (which is not possible, as the radius can't be negative)
Therefore, the given information might be incorrect or there might be an error in the image.