Question

the height of the cylinder is 8 centimeters. the volume of the cylinder is 72π cubic centimeters. what is the length, in centimeters, of (overline{bc})? (sqrt{55}) (sqrt{93}) 10 11

Explanation:

Step1: Find the radius of the cylinder

The volume formula of a cylinder is \(V=\pi r^{2}h\). Given \(V = 72\pi\) and \(h = 8\). Substitute into the formula:
\(72\pi=\pi r^{2}\times8\). Divide both sides by \(8\pi\): \(r^{2}=\frac{72\pi}{8\pi}=9\), so \(r = 3\).

Step2: Use the Pythagorean theorem to find \(BC\)

In the right - triangle \(BCD\) (where \(CD\) is the height of the cylinder \(h = 8\) and \(BD\) is the diameter of the base \(d = 2r=6\)). By the Pythagorean theorem \(BC=\sqrt{BD^{2}+CD^{2}}\). Substitute \(BD = 6\) and \(CD = 8\): \(BC=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\).

Answer:

C. 10