Question

use the formula ( v = pi r ^ { 2 } h ) for the volume. (remember the radius is half of the diameter.)

a ( v = 175.93 mathrm { in } ^ { 3 } )
b ( v = 80 mathrm { in } ^ { 3 } )
c ( v = 703.72 mathrm { in } ^ { 3 } )

Explanation:

Step1: Find the radius

The diameter is \(4\) in. Since \(r=\frac{d}{2}\), then \(r = \frac{4}{2}=2\) in.

Step2: Substitute into the volume formula

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 2\) in and \(h=14\) in. So \(V=\pi\times(2)^{2}\times14\).
First, calculate \((2)^{2}=4\). Then \(V=\pi\times4\times14 = 56\pi\).
Take \(\pi\approx3.14\), so \(V=56\times3.14 = 175.84\approx175.93\) \(in^{3}\).

Answer:

A. \(V = 175.93\ in^{3}\)