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

14.1 cm
14.1 cm

18.0 cm
18.0 cm

11.2 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.

In a cylinder, the diagonal \( d \) acts as the hypotenuse of a right triangle where one leg is the height \( h \) and the other leg is the diameter of the base, which is \( 2r \).

The relationship can be expressed as:

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

Substituting the known values:

\[
15^2 = h^2 + (2 \times 5)^2
\]

Calculating \( 15^2 \) and \( (2 \times 5)^2 \):

\[
225 = h^2 + 100
\]

Now, isolating \( h^2 \):

\[
h^2 = 225 - 100
\]
\[
h^2 = 125
\]

Taking the square root of both sides:

\[
h = \sqrt{125} \approx 11.2 \text{ cm}
\]

So, the height \( h \) of the cylinder is approximately \( 11.2 \) cm.

Therefore, the answer is:

**11.2 cm**