Question

Use the image to answer the 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 14.1 cm 14.1 cm - incorrect 18.0 cm 18.0 cm - no response given 15.8 cm 15.8 cm - no response given 11.2 cm 11.2 cm - no response given Remaining Attempts : 2

Answer 1

To find the height \( h \) of the cylinder using the radius \( r \) and the diagonal \( d \), we can use the Pythagorean theorem. The diagonal of the cylinder (in this context) forms a right triangle with the height and the radius.

The relationship can be expressed as:

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

Given:
- The radius \( r = 5 \) cm
- The diagonal \( d = 15 \) cm

Substituting the values into the equation:

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

Calculating the squares:

\[
225 = h^2 + 25
\]

Now, subtract 25 from both sides:

\[
225 - 25 = h^2
\]

\[
200 = h^2
\]

Take the square root of both sides to find \( h \):

\[
h = \sqrt{200}
\]

Calculating \( \sqrt{200} \):

\[
h \approx 14.14
\]

Rounding this to the nearest tenth gives:

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

So the correct answer for the height \( h \) of the cylinder is approximately **14.1 cm**.