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Item 21 In your pottery class, you are given a lump of clay with a volume of 200 cubic centimeters and are 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 of the clay

Respuesta :

Answer: The thickness of his pencil holder would be 1 cm.

Step-by-step explanation:

Since we have given that

Volume of lump of clay = 200 cubic cm

Height of pencil holder = 9 cm

Radius of pencil holder = 3 cm

Let the thickness of pencil holder be 'x'.

As we know the formula for "Volume of pipe":

[tex]Volume=\pi (R^2-r^2)h\\\\200=\dfrac{22}{7}(R^2-9)\times 9\\\\1400=22\times 9(R^2-9)\\\\1400=198(R^2-9)\\\\\dfrac{1400}{198}=R^2-9\\\\7.07+9=R^2\\\\16.07=R^2\\\\R=\sqrt{16.07}\\\\R=4.008\\\\R\approx 4[/tex]

Since x = R-r

x = 4-3

x=1 cm

Hence, the thickness of his pencil holder would be 1 cm.

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