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

3.0 ft.
3.0 ft.

12.8 ft.
12.8 ft.

6.4 ft.
6.4 ft.

6.0 ft.

Answer 1

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

We have a cylinder with:

• Height (h) = 8 ft (the height of the container)
• Length of the pole (l) = 10 ft

For the pole to fit perfectly on the diagonal, we can visualize a right triangle where:

• One leg of the triangle is the height of the cylinder (8 ft).
• The other leg of the triangle is the diameter of the cylinder (which is twice the radius, or 2r).
• The hypotenuse of the triangle is the length of the pole (10 ft).

Using the Pythagorean theorem, we have:

\[ (l)^2 = (h)^2 + (diameter)^2 \]

Substituting the values we have:

\[ 10^2 = 8^2 + (2r)^2 \]

Calculating further:

\[ 100 = 64 + (2r)^2 \]

Subtracting 64 from both sides:

\[ 100 - 64 = (2r)^2 \] \[ 36 = (2r)^2 \]

Now, taking the square root of both sides:

\[ 6 = 2r \]

Dividing both sides by 2 gives:

\[ r = 3 \]

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