Answer:
Step-by-step explanation:
The way I am seeing this is that you have to take the surface area of the whole cylinder (the one with the diameter of 6) and subtract from it the surface area of the inner cylinder (the one with the diameter of 4) in order to get how much concrete you need to get that "outer shell" of concrete.
The surface area formula, regardless of the size of the cylinder, is:
[tex]SA=2\pi rh+2\pi r^2[/tex]
The diameter of the bigger cylinder has a diameter of 6; therefore, it has a radius of 3. We will state the answer in 2 ways: one with the answer in terms of pi, and then figuring in pi as a decimal equal to 3.1415.
The surface area of the bigger cylinder first:
[tex]SA=2\pi (3)(6)+2\pi (9)[/tex]
The surface area, when you add these 2 like terms together is
[tex]SA=54\pi[/tex]
Now for the smaller, inner, cylinder:
[tex]SA=2\pi (2)(6)+2\pi (4)[/tex]
Th surface area, when you add these 2 like terms together is
[tex]SA=32\pi[/tex]
The bigger minus the smaller gives you a surface area of
[tex]SA=22\pi yd^3[/tex]
which has a decimal equivalency of
[tex]SA=69.113yd^3[/tex]
