Find the height, h, of the cylinder. The radius is
6 cm and the diagonal, d, is 14 cm. Round the
answer to the nearest tenth.
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.