A solid wooden cylinder of height 8 cm and radius 3 cm is cut in two along a vertical axis of symmetry. Calculate the total surface area of the two pieces.
Answers
Answer:The surface are of a cylinder is
SA = 2πr2 + 2πrh
where:
r = radius
h = height
This formula comes from adding the areas of the surfaces of the cylinder. It has two flat circular faces and a rounded face.
If we cut the cylinder from the circular face symmetrically, the surface area for one piece will be
SA = 2[(πr2)/2] + (2πr/2)h + 2rh
We will have 2-half flat circular faces, a flat rectangular surface, and half of the rounded surface.
Simplify the SA formula.
SA = πr2 + πrh + 2rh
SA = r(πr + πh + 2h)
Substitute the values into this formula.
SA = 3(3π + 8π + (2*8))
SA = 3(11π + 16)
SA = 33π + 48
SA = 151.67 cm2
Since we have 2 pieces, multiply this result by 2.
2(151.67 cm2) = 303.34 cm2.
The total area is 303.34 cm2
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