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.
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.