Question

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?

(1 point)
Responses

12
12

10
10

4
4

8
8
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Answer 1

To find the radius of the cone, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the lengths of the other two sides.

In this case, one of the other sides is the radius of the cone and the hypotenuse is the slant height of the cone. We can use the given information to set up an equation:

radius^2 + height^2 = slant height^2

Substituting the given values into the equation:

radius^2 + 12^2 = 10^2

Solving for the radius:

radius^2 + 144 = 100

radius^2 = 100 - 144

radius^2 = -44

Since the radius cannot be a negative value, we can conclude that there must be an error in the given information or the diagram. Without further information, we are unable to determine the radius of the cone.