Question

Question

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)
Responses

6.0 ft
6.0 ft

3.0 ft
3.0 ft

12.8 ft
12.8 ft

6.4 ft

Answer 1

To determine the radius needed for the pole to fit perfectly on the diagonal of the cylindrical container, we can visualize the problem as a right triangle where:

• One leg is the height of the container (8 ft),
• The other leg is the diameter of the base of the cylinder (which is double the radius),
• The hypotenuse is the length of the pole (10 ft).

Let's denote the radius of the container as \( r \). Therefore, the diameter would be \( 2r \).

According to the Pythagorean theorem:

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

Calculating the squares:

\[ 100 = 64 + 4r^2 \]

Subtract 64 from both sides:

\[ 36 = 4r^2 \]

Now, divide both sides by 4:

\[ 9 = r^2 \]

Taking the square root of both sides gives:

\[ r = 3 \]

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

Therefore, the correct answer is 3.0 ft.