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)

Explanation:

Step1: Find the diameter

The diameter \(D = 2r\). Given \(r = 5\) cm, so \(D=2\times5 = 10\) cm.

Step2: Apply the Pythagorean theorem

In the right - triangle formed by the height \(h\), diameter \(D\), and diagonal \(d\) of the cylinder, by the Pythagorean theorem \(d^{2}=h^{2}+D^{2}\). We need to solve for \(h\), so \(h=\sqrt{d^{2}-D^{2}}\). Substitute \(d = 15\) cm and \(D = 10\) cm. Then \(h=\sqrt{15^{2}-10^{2}}=\sqrt{225 - 100}=\sqrt{125}\).

Step3: Calculate the value

\(\sqrt{125}\approx11.2\) (rounded to the nearest tenth).

Answer:

\(11.2\) cm