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)

Answer 1

wrong

Answer 2

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.

Answer 3

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.