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)
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.
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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.
To find the height of the cylinder, we can use the Pythagorean theorem because the diameter of the base and the height of the cylinder form a right triangle.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
In this case, the radius of the base is one leg, the height of the cylinder is the other leg, and the diagonal is the hypotenuse.
Using the formula of the Pythagorean theorem: a^2 + b^2 = c^2, where 'a' and 'b' are the legs and 'c' is the hypotenuse, we can write:
r^2 + h^2 = d^2
Substituting the given values, we have:
(5 cm)^2 + h^2 = (15 cm)^2
Simplifying the equation:
25 cm^2 + h^2 = 225 cm^2
Rearranging the equation to solve for h^2:
h^2 = 225 cm^2 - 25 cm^2
h^2 = 200 cm^2
To find the height, we take the square root of both sides:
h = √(200 cm^2)
Calculating h:
h ≈ 14.1 cm
Therefore, the height of the cylinder, h, is approximately 14.1 cm rounded to the nearest tenth.