AL Athletics makes poles for pole vaulting. They use cylinder-shaped containers for shipping. If the company is mailing a pole that is 10 ft. in length in a container that has a height of 8 ft., what radius is needed for the pole to fit perfectly on the diagonal? Round the answer to the nearest tenth. (1 point)

Question

Responses

6.0 ft.
6.0 ft.

12.8 ft.
12.8 ft.

3.0 ft.
3.0 ft.

6.4 ft.
6.4 ft.
Remaining Attempts : 3

Answer 1

To determine the radius needed for the pole to fit perfectly on the diagonal of the cylinder-shaped container, we can use the Pythagorean theorem.

In this case, we have a right triangle formed by the height of the container, the length of the pole, and the diagonal of the container. The height of the container is 8 ft., and the length of the pole is 10 ft. We can denote the radius of the container as $r$.

The diagonal $d$ can be computed using the Pythagorean theorem in a 2D plane, which states:

$$d=\sqrt{(height{)}^2+(diameter{)}^2}$$

In terms of the radius, the diameter $D$ is $2r$. Therefore:

$$d=\sqrt{(8{)}^2+(2r{)}^2}$$

We want the length of the pole (10 ft) to equal the diagonal $d$:

$$10=\sqrt{8^2+(2r{)}^2}$$

Now, squaring both sides:

$$100=64+4r^2$$

Now, we can isolate $r^2$:

$$100-64=4r^2$$ $$36=4r^2$$ $$9=r^2$$

Taking the square root of both sides:

$$r=3\text{ ft}$$

Thus, the required radius for the pole to fit perfectly on the diagonal is 3.0 ft.