SOLUTION: 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 holde

Question 178865: 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?
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
Q: Pottery You are taking a pottery class. As an assignment, you are given a lump of clay whose volume is 200 cubic cetimeters and asked to make a cylindrical pencil holder. The pencil holder should be 9 centimeters high and have an inner radius of 3 centimeters. 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.)
Ans:
Total Volume of hollow cylender V = 200 cc
Inner radius Ri = 3 Cm
Outer Radius Ro = r (Assume it)
Height of cylinder = 9 cm
:
Volume of Hollow Cylinder=Volume of Outer Cylinder - Volume Of inner Cylinder
so 200 = Pi*Ro*Ro*9 - Pi*Ri*Ri*9
= Pi*9(Ro*Ro - 3*3)
200/(3.14*9)= Ro*Ro -9
200/28.26 + 9 = Ro*Ro
7.077 + 9 = Ro*Ro
16.077 = Ro*Ro
4 = Ro ----------(Taking square Root )
:
So thickness of the Cylinder = Ro-Ri (Outer Radius - Inner Radius)
= 4 - 3
= 1 cm

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