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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
ok........we know that the volume of the cylinder is %28pi%29r%5E2h
so what we need is to take the outer volume9%28pi%29r%5E2 and subtract out the inner volume %28pi%293%5E2%289%29 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 %28pi%29
:
9%28pi%29r%5E2-%28pi%293%5E2%289%29=200
28.26r%5E2-254.34=200
28.26r%5E2=454.34
r%5E2=16
r=4cm...this isnt exactly 4 because of approximations
highlight%284-3=1%29cm....thickness of pencil holder

Answer by scott8148(6628) About Me  (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