Question

what is the volume of a cylindrical ring if we know the diameter of the revolving circle is 4 ft. and the length of the center line is 65 ft.?
a) 567.94 ft.³
b) 816.82 ft.³
c) 624.33 ft.³
d) 488.20 ft.³

Explanation:

Step1: Find the radius of the revolving circle

The diameter of the revolving circle \(d = 4\) ft, so the radius \(r=\frac{d}{2}=\frac{4}{2}=2\) ft.

Step2: Use the formula for the volume of a toroid (cylindrical ring)

The formula for the volume of a toroid is \(V=\pi r^{2}L\), where \(r\) is the radius of the revolving circle and \(L\) is the length of the center - line.
Substitute \(r = 2\) ft and \(L=65\) ft into the formula:
\(V=\pi\times(2)^{2}\times65\)
\(V=\pi\times4\times65\)
\(V = 260\pi\)
Take \(\pi\approx3.1416\), then \(V\approx260\times3.1416 = 816.816\approx816.82\) \(ft^{3}\)

Answer:

B) \(816.82\) \(ft^{3}\)