**Answer:**

**Step-by-step explanation:**

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