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The neighborhood association is buying timbers to put around the edge of the playground. The length of the playground is 51 1/8
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This question is incomplete; here is the complete question.
A closed cylindrical can of fixed volume V has radius r. (a) Find the surface area, S, as a function of r. (b) What happens to the value of S approaches to infinity? (c) Sketch a graph of S against r, if V=10 cm³.
A closed cylindrical can of volume V is having radius r and height h.
a). Surface area of a cylinder is given by
S = 2(Area of the circular sides) + Lateral area of the can
S = 2πr² + 2πrh
S = 2πr(r + h)
b). Since surface area is directly proportional to radius of the can
S ∝ r
Therefore, when r approaches to infinity (r → ∞)
c). If V = 10 cm³ Then we have to graph S against r.
From the formula V = πr²h
10 = πr²h
h =
By placing the value of h in the formula of surface area,
S =
Now we can get the points to plot the graph,
r -2 -1 0 1 2
S -13.72 -13.72 0 26.28 35.13
