Find the height, h, of the cylinder. The radius, r, is 5 cm and the diagonal, d, is 15 cm. Round the answer to the nearest tenth.

Answer 1

To find the height $h$ of the cylinder given the radius $r=5$ cm and the diagonal $d=15$ cm, we can use the Pythagorean theorem. The diagonal of the cylinder can be thought of as the hypotenuse of a right triangle where one leg is the height $h$ and the other leg is the diameter of the base of the cylinder.

1. First, calculate the diameter of the base: $$\text{Diameter}=2r=2\times 5=10\text{ cm}$$

2. Next, set up the Pythagorean theorem where $d$ is the hypotenuse, the height $h$ is one leg, and the diameter is the other leg: $$d^2=h^2+{\text{Diameter}}^2$$

3. Substituting the known values: $${15}^2=h^2+{10}^2$$ $$225=h^2+100$$

4. Rearranging the equation to solve for $h^2$: $$h^2=225-100$$ $$h^2=125$$

5. Taking the square root to find $h$: $$h=\sqrt{125}\approx 11.1803$$

6. Rounding to the nearest tenth: $$h\approx 11.2\text{ cm}$$

Thus, the height $h$ of the cylinder is approximately $\boxed{{\displaystyle 11.2}}$ cm.