SOLUTION: 93. You are taking a pottery class. As an assignment, you are given a lump of clay whose volume is 200 cubic centimeters and asked to make a cylindrical pencil holder. The pencil

Question 171431This question is from textbook Algebra 2
: 93. You are taking a pottery class. As an assignment, you are given a lump of clay whose volume is 200 cubic centimeters and asked to make a cylindrical pencil holder. The pencil holder should be 9 cm high and have an inner radius of 3 cm. What thickness "x" should your pencil holder have if you want to use all the clay? (hint: the volume of clay equals the difference of the volumes of two cylinders.)
The answer in the back of the book is "about" 1 cm but i dont know why. Should i use completing the square? ive tried all the cylinder equations and nothing gives me 1. This question is from textbook Algebra 2

Found 2 solutions by Mathtut, scott8148:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
ok........we know that the volume of the cylinder is
so what we need is to take the outer volume and subtract out the inner volume to get the thickness volume. we know that the volume of the clay(200) will be equal to outer volume-inner volume.
We also know that the outer radius which is the unknown here minus the inner radius will give the measurement of the thickness of the pencil holder. I used 3.14 as appx value of
:

cm...this isnt exactly 4 because of approximations
cm....thickness of pencil holder
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the two cylinders are the hollow inside and the outside of the holder

if the thickness is x and the inner radius is 3 then the outer radius is 3+x

volume is πr^2h

[π * (3+x)^2 * 9] - [π * 3^2 * 9] = 200

dividing by 9π __ x^2+6x = 200/(9π) = 7.074 (approx)

completing the square __ x^2+6x+9 = 16.074

taking square root __ x+3 = �4.009 (approx)

x=1.009 (about one) and x=-7.009
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