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.
(1 point)
Responses

15.8 cm
15.8 cm
11.2 cm
11.2 cm
18.0 cm
18.0 cm
14.1 cm

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 forms a right triangle with the height and the diameter of the base of the cylinder.

First, we need to find the diameter \( D \) of the cylinder:

\[
D = 2r = 2 \times 5 = 10 \text{ cm}
\]

Now, we can apply the Pythagorean theorem to the right triangle formed by the height \( h \), the radius (half of the diameter) \( r \), and the diagonal \( d \):

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

Substituting the values we have:

\[
15^2 = h^2 + 5^2
\]
\[
225 = h^2 + 25
\]

Now, we solve for \( h^2 \):

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

Taking the square root of both sides gives:

\[
h = \sqrt{200} \approx 14.1 \text{ cm}
\]

Rounding to the nearest tenth, the height \( h \) is approximately:

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

Thus, the correct response is:

**14.1 cm**