College algebra

Question

A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8pi ft squared. What should the radius of the circular top and bottom of the container be? (Hint: the surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled.)

Answer 1

SA of cylinder = 8 pi

factor

radius = 1 ft

Answer 2

You are given the height and surface area of a cylinder and have to find the radius of the cylinder.

 

So start out by writing the formula for the surface area of a cylinder.

 

Surface Area =  2 Π r²  +  2 π r h                    (π = pi , r= radius   h= height)

 

 

Plug in the values you have, then solve for the radius r.

 

8 π  =  2 Π r²   +   2 π r 3

 

8π  =   2 Π r^{2   +}  6 Π r                              Divide all terms by 2π 

 

4  =  r²  +  3r                         The highest power is 2 so you have a quadratic equation,  try to solve                                                                                    by factoring

 

r² + 3r - 4 = 0         Factor the trinomial.  The 2 first terms would be x and  the second terms would have to satisfy these conditions : two numbers with opposite signs , factors of 4 and must add up to 3. Since the middle term is positive , that means the number with the greater absolute value must be positive.

 

(r  +  4)  ( r - 1)  = 0

 

r = -4  or  r = 1   we know a radius cannot be negative, so -4 is an extraneous solution.

 

The radius of the cylinder is 1 ft.

 

If you check your answer and plug in 1 for the radius and use the surface area formula , you will get 8π.

 

 

Answer 3

surface area = circumference · height

8π = 3c

8π/3 = c

 

c = 2πr

8π/3 = 2πr

8/3 = 2r

8/6 = r

4/3 = r