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General
Easy

Question

A drainage tile is a cylindrical shell 21 cm long. The inside and outside diameters are 4.5 cm and 5.1 cm respectively. What is the volume of the clay required for the tile?

hintHint:

Subtracting the volume of the shell with inner radius from the volume with outer radius would give us the volume of clay required for the tile.

The correct answer is: The volume of the clay required for the tile is 95.04 cm3


    Explanations:
    Step 1 of 2:
    Given, h = 21cm; r = 4.5/2 cm (inner radius) and R  = 5.1/2 cm (outer radius)
    The volume with inner radiusequals pi r squared h equals pi open parentheses fraction numerator 4.5 over denominator 2 end fraction close parentheses squared 21 cm3
    The volume with outer radius = pi R squared h equals pi open parentheses fraction numerator 5.1 over denominator 2 end fraction close parentheses squared 21  cm3
    Step 2 of 2:
    The volume of the clay required for the tile
    pi R squared h minus pi r squared h
    equals pi open parentheses R squared minus r squared close parentheses h
    equals pi left parenthesis R plus r right parenthesis left parenthesis R minus r right parenthesis h
    equals 22 over 7 cross times open parentheses fraction numerator 5.1 over denominator 2 end fraction plus fraction numerator 4.5 over denominator 2 end fraction close parentheses cross times open parentheses fraction numerator 5.1 over denominator 2 end fraction minus fraction numerator 4.5 over denominator 2 end fraction close parentheses cross times 21
    equals 22 over 7 cross times 1 half left parenthesis 5.1 plus 4.5 right parenthesis cross times 1 half left parenthesis 5.1 minus 4.5 right parenthesis cross times 21
    equals 95.04 cm cubed
    Final Answer:
    The volume of the clay required for the tile is 95.04 cm3
     

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