First, let's calculate the diagonal of the cylinder-shaped container using the Pythagorean theorem:
Diagonal^2 = 10^2 + 8^2
Diagonal^2 = 100 + 64
Diagonal^2 = 164
Diagonal = sqrt(164)
Diagonal ≈ 12.8 ft
Now, the diagonal of the cylinder is equal to the diameter of the base of the cylinder. Since the pole will be standing upright in the cylinder, the radius equals half of the diameter:
Diameter = 2 * Radius
12.8 = 2 * Radius
Radius = 12.8 / 2
Radius = 6.4 ft
Therefore, a radius of 6.4 ft is needed for the pole to fit perfectly on the diagonal of the cylinder. Rounded to the nearest tenth, the answer is 6.4 ft.
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 p
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nope
Let's correct the solution:
To find the diagonal (diameter) of the cylindrical container, we can use the formula:
Diagonal = sqrt(10^2 + 8^2)
Diagonal = sqrt(100 + 64)
Diagonal = sqrt(164)
Diagonal ≈ 12.81 ft
The diameter of the cylinder is equal to the diagonal, so the radius is half of the diagonal:
Radius = 12.81 / 2
Radius ≈ 6.4 ft
Therefore, the radius needed for the pole to fit perfectly on the diagonal of the container is approximately 6.4 ft.
To find the diagonal (diameter) of the cylindrical container, we can use the formula:
Diagonal = sqrt(10^2 + 8^2)
Diagonal = sqrt(100 + 64)
Diagonal = sqrt(164)
Diagonal ≈ 12.81 ft
The diameter of the cylinder is equal to the diagonal, so the radius is half of the diagonal:
Radius = 12.81 / 2
Radius ≈ 6.4 ft
Therefore, the radius needed for the pole to fit perfectly on the diagonal of the container is approximately 6.4 ft.
The Pythagorean Theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.
You are correct, the Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Given that the container is in the shape of a cylinder and we are looking for the diagonal length of the cylinder, we would calculate it as follows:
Diagonal^2 = Height^2 + Radius^2 (assuming the pole is to be placed diagonally across the cylinder)
Using the given values:
Diagonal^2 = 8^2 + Radius^2
Diagonal^2 = 64 + Radius^2
Since the length of the pole is 10 ft, the diagonal will be equal to the length of the pole:
10^2 = 64 + Radius^2
100 = 64 + Radius^2
36 = Radius^2
Radius = sqrt(36)
Radius = 6 ft
Therefore, a radius of 6 ft is needed for the pole to fit diagonally in the cylinder-shaped container.
Given that the container is in the shape of a cylinder and we are looking for the diagonal length of the cylinder, we would calculate it as follows:
Diagonal^2 = Height^2 + Radius^2 (assuming the pole is to be placed diagonally across the cylinder)
Using the given values:
Diagonal^2 = 8^2 + Radius^2
Diagonal^2 = 64 + Radius^2
Since the length of the pole is 10 ft, the diagonal will be equal to the length of the pole:
10^2 = 64 + Radius^2
100 = 64 + Radius^2
36 = Radius^2
Radius = sqrt(36)
Radius = 6 ft
Therefore, a radius of 6 ft is needed for the pole to fit diagonally in the cylinder-shaped container.
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1 answer