Find the height, h, of the cylinder. The radius is

Question

6 cm and the diagonal, d, is 14 cm. Round the
answer to the nearest tenth.

Answer 1

We can start by finding the length of the cylindrical surface using the formula for the circumference of a circle:

C = 2πr

In this case, the radius is 6 cm, so

C = 2π(6) = 12π cm

Next, we can find the height using the Pythagorean theorem. We know that the diagonal, d, is equal to the hypotenuse of a right triangle with the height h as one of the legs and the radius r as the other leg. So the equation is:

d^2 = h^2 + r^2

Substituting the given values:

14^2 = h^2 + 6^2

196 = h^2 + 36

Now we can solve for h.

h^2 = 196 - 36

h^2 = 160

Taking the square root of both sides:

h = √160 ≈ 12.65

Rounding to the nearest tenth:

h ≈ 12.7 cm

So, the height of the cylinder is approximately 12.7 cm.