Question

13 multiple choice 1 point find the volume of a cylinder (in cubic feet) which is 1 1/2 feet high and has a diameter of 8 inches. (leave answer in terms of π.) 6πft³ 1/6 πft³ 2/3 πft³ 12πft³ 14 multiple choice 1 point this drawing is an example of a ________. octagon reflection rotation translation

Explanation:

Step1: Convert units

The diameter \(d = 8\) inches. Since \(1\) foot \(= 12\) inches, the radius \(r=\frac{d}{2}=\frac{8}{2}\) inches \( = 4\) inches. Converting radius to feet: \(r=\frac{4}{12}=\frac{1}{3}\) feet. The height \(h = 1\frac{1}{2}=\frac{3}{2}\) feet.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). Substitute \(r = \frac{1}{3}\) and \(h=\frac{3}{2}\) into the formula: \(V=\pi\times(\frac{1}{3})^{2}\times\frac{3}{2}\).

Step3: Simplify the expression

First, \((\frac{1}{3})^{2}=\frac{1}{9}\). Then \(V=\pi\times\frac{1}{9}\times\frac{3}{2}\). Multiply \(\frac{1}{9}\times\frac{3}{2}=\frac{1\times3}{9\times2}=\frac{1}{6}\). So \(V = \frac{1}{6}\pi\) cubic feet.

Answer:

\(\frac{1}{6}\pi\mathrm{ft}^{3}\) (the second option)