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.

Answer 1

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.