Question
Find the height, h , of the cylinder. The radius, r , is 5 cm and the diagonal, d , is 15 cm. Round the answer to the nearest tenth. (1 point)
Answers
GPT 3.5
We can use the Pythagorean theorem to solve this problem.
The diagonal of the cylinder is the hypotenuse of a right triangle. The height of the cylinder is one leg of the right triangle, and the radius of the cylinder is the other leg. So we have a right triangle with legs measuring 5 cm and h cm, and a hypotenuse measuring 15 cm.
Using the Pythagorean theorem, we can write the equation:
(5 cm)^2 + h^2 = (15 cm)^2
25 cm^2 + h^2 = 225 cm^2
Rearranging the equation, we have:
h^2 = 225 cm^2 - 25 cm^2
h^2 = 200 cm^2
Taking the square root of both sides, we get:
h ≈ √200 cm
h ≈ 14.1 cm
Therefore, the height of the cylinder is approximately 14.1 cm.
The diagonal of the cylinder is the hypotenuse of a right triangle. The height of the cylinder is one leg of the right triangle, and the radius of the cylinder is the other leg. So we have a right triangle with legs measuring 5 cm and h cm, and a hypotenuse measuring 15 cm.
Using the Pythagorean theorem, we can write the equation:
(5 cm)^2 + h^2 = (15 cm)^2
25 cm^2 + h^2 = 225 cm^2
Rearranging the equation, we have:
h^2 = 225 cm^2 - 25 cm^2
h^2 = 200 cm^2
Taking the square root of both sides, we get:
h ≈ √200 cm
h ≈ 14.1 cm
Therefore, the height of the cylinder is approximately 14.1 cm.
wrong
GPT 3.5
I apologize for the mistake. Let's correct it:
We can use the Pythagorean theorem to solve this problem.
The diagonal of the cylinder is the hypotenuse of a right triangle. The height of the cylinder is one leg of the right triangle, and the radius of the cylinder is the other leg. So we have a right triangle with legs measuring r cm and h cm, and a hypotenuse measuring d cm.
Using the Pythagorean theorem, we can write the equation:
r^2 + h^2 = d^2
(5 cm)^2 + h^2 = (15 cm)^2
25 cm^2 + h^2 = 225 cm^2
Subtracting 25 cm^2 from both sides, we get:
h^2 = 200 cm^2
Taking the square root of both sides, we get:
h ≈ √200 cm
h ≈ 14.1 cm
Therefore, the height of the cylinder is approximately 14.1 cm.
We can use the Pythagorean theorem to solve this problem.
The diagonal of the cylinder is the hypotenuse of a right triangle. The height of the cylinder is one leg of the right triangle, and the radius of the cylinder is the other leg. So we have a right triangle with legs measuring r cm and h cm, and a hypotenuse measuring d cm.
Using the Pythagorean theorem, we can write the equation:
r^2 + h^2 = d^2
(5 cm)^2 + h^2 = (15 cm)^2
25 cm^2 + h^2 = 225 cm^2
Subtracting 25 cm^2 from both sides, we get:
h^2 = 200 cm^2
Taking the square root of both sides, we get:
h ≈ √200 cm
h ≈ 14.1 cm
Therefore, the height of the cylinder is approximately 14.1 cm.