Height-4 Width-5 Base-6
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First take the top and bottom discs, which each have an area of (pi)r^2. The surface area of the curved side is 2(pi)rh  (circumference times height) where r=radius and h=height. So the total surface area is 2(pi)r(r+h). But which value do we use for the width? If we use the base, r=3 because the base=diameter=2r. The surface area is 2*(pi)*3*7=42(pi)=131.95 cubic units. If we use the width, r=2.5 and the surface area is 2*(pi)*2.5*6.5=32.5(pi)=102.10. If the width is the thickness of a hollow cylinder we take the difference between the inner and outer top and bottom circles=2(pi)(3^2-2.5^2)=5.5(pi). The outer surface area is 2(pi)*3*4=24(pi) and the inner surface area is 2(pi)*2.5*4=20(pi). These curved surface areas have to be added together=44(pi). Altogether then the total surface area is (5.5+44)(pi)=49.5(pi)=155.51 cubic units.

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