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Find the height, h%0D%0Aℎ%0D%0A, of the cylinder. The radius, r%0D%0A%0D%0A, is 5 cm and the diagonal, d%0D%0A%0D%0A, is 15 cm. Round the answer to the nearest tenth.
Answers
GPT 3.5
To find the height of the cylinder, we can use the Pythagorean theorem. The diagonal of the cylinder (d) is the hypotenuse of a right triangle formed by the height (h) and the radius (r).
Using the Pythagorean theorem, we have:
d^2 = h^2 + r^2
Substituting the given values, we have:
15^2 = h^2 + 5^2
225 = h^2 + 25
Subtracting 25 from both sides:
200 = h^2
Taking the square root of both sides:
h = √200
h ≈ 14.14 cm
Rounding to the nearest tenth, the height of the cylinder is approximately 14.1 cm.
Using the Pythagorean theorem, we have:
d^2 = h^2 + r^2
Substituting the given values, we have:
15^2 = h^2 + 5^2
225 = h^2 + 25
Subtracting 25 from both sides:
200 = h^2
Taking the square root of both sides:
h = √200
h ≈ 14.14 cm
Rounding to the nearest tenth, the height of the cylinder is approximately 14.1 cm.