SOLUTION: Hello, the following problem involves with finding the radius of a cylinder with just the surface area given. I tried plugging in these values but the book has a different answer.

Algebra ->  Linear-equations -> SOLUTION: Hello, the following problem involves with finding the radius of a cylinder with just the surface area given. I tried plugging in these values but the book has a different answer.       Log On


   

Question 967660: Hello, the following problem involves with finding the radius of a cylinder with just the surface area given. I tried plugging in these values but the book has a different answer. Could someone please help with clarification.
Here is the problem:
S = 2πrh
Given values are:
S = 120π, h = 10
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you are given that S = 2 * pi * r * h.

that would be the lateral area only.

it does not include the area of the bases.

if the formula you show is the formula you are given, then:

S = 2 * pi * r * h becomes 120 = 2 * pi * r * 10.

simplify to get 120 = 20 * pi * r

divide both sides of the equation by (20 * pi) and you get:

120 / (20 * pi) = r

solve for r to get r = 6 / pi.

you can leave it that way or you can simplify further to get r = 1.909859317.

you can confirm by replacing r with 1.909859317 and you will get 120 = 120.

now, the surface area of of a right cylinder is equal to the lateral area plus the base area.

that formula is S = 2 * pi * r * h + 2 * pi * r^2.

that's going to make a difference in what the radius turns out to be.

if that's the formula you need, then:

S = 2 * pi * r * h + 2 * pi * r^2 becomes:

120 = 2 * pi * r * 10 + 2 * pi * r^2

simplify to get:

120 = 20 * pi * r + 2 * pi * r^2

subtract 120 from both sides of the equation and re-arrange the terms and commute the equation to get:

2 * pi * r^2 + 20 * pi * r - 120 = 0

that's a quadratic equation in standard form that can be solved using the quadratic formula.

you will get:

Roots: -11.64067716, 1.640677162

negative value is no good.

r has to be 1.640677162 if we did everything correctly.

confirm by replacing that value of r in the original equation with 1.640677162 and you will see that the surface area is equal to 120.

here's an online calculator to give you the surface area of cylinder.

https://www.google.com?gws_rd=ssl#q=surface+areea+of+a+cylinder

here's what the output looks like after you enter 1.64...... for the radius and 10 for the height.

$$$

the quadratic formula is: 


               (-b plus or minus sqrt(b^2 - 4ac)
         x =   -----------------------------------
                                (2a)


your quadratic equation is :

2 * pi * r^2 + 20 * pi * r - 120 = 0

a = 2 * pi
b = 20 * pi
c = -120