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 as r approaches infinity? 0,1, or infinity

Answer 1

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 = $\frac{10}{\pi r^{2}}$

By placing the value of h in the formula of surface area,

S = $2\pi r(r+\frac{10}{\pi r^{2}})$

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