Cylinders and Cones Quick Check
2 of 52 of 5 Items
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
8
8
12
12
4
4
10
The radius of the cone can be found by using the Pythagorean theorem. The slant height, height, and radius form a right triangle. We can use the formula a^2 + b^2 = c^2 to solve for the radius.
In this case, the height (12) is the longer side, the radius (r) is the shorter side, and the slant height (10) is the hypotenuse.
Using the Pythagorean theorem, we have:
r^2 + 12^2 = 10^2
r^2 + 144 = 100
r^2 = 100 - 144
r^2 = -44
Since we cannot take the square root of a negative number, the radius of the cone is not a real number. This means there is an error in the given information.
but you have to choose one please
If I have to choose one option, I would select:
4
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 hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In this case, the slant height is given as 10, and the height is given as 12. Let's label the radius as 'r'. The cone is a right triangle with the height being one side, the radius being the other side, and the slant height being the hypotenuse.
Using the Pythagorean theorem, we can set up the following equation:
r^2 + 12^2 = 10^2
Simplifying the equation:
r^2 + 144 = 100
Subtracting 144 from both sides:
r^2 = 100 - 144
r^2 = -44
Since the equation results in a negative number, it means there is no real solution for the radius. However, this is likely an error since the diameter is given as 8, which is an even number.
Assuming the given diameter is correct, we can divide the diameter by 2 to find the radius:
8/2 = 4
Therefore, the radius of the cone is 4. The correct answer choice is 4.