Question

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.

18.0 cm
11.2 cm
15.8 cm
14.1 cm

Answer 1

To find the height \( h \) of the cylinder, we can use the relationship between the radius \( r \), height \( h \), and the diagonal \( d \) (which is the slant height of the cylinder). The relationship is derived from the Pythagorean theorem, as the diagonal forms a right triangle with the height and the radius:

\[
d^2 = r^2 + h^2
\]

Here, we have:

- \( d = 15 \) cm
- \( r = 5 \) cm

First, we square \( d \) and \( r \):

\[
d^2 = 15^2 = 225
\]
\[
r^2 = 5^2 = 25
\]

Now we can substitute these values into the equation:

\[
225 = 25 + h^2
\]

Next, solve for \( h^2 \):

\[
h^2 = 225 - 25
\]
\[
h^2 = 200
\]

Now take the square root to find \( h \):

\[
h = \sqrt{200}
\]
\[
h = \sqrt{100 \times 2} = 10\sqrt{2} \approx 10 \times 1.414 \approx 14.14
\]

Rounding to the nearest tenth, we find:

\[
h \approx 14.1 \text{ cm}
\]

Therefore, the height of the cylinder \( h \) is \( \boxed{14.1} \) cm.