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Easy

Question

The inner diameter of a cylindrical wooden pipe is 24 cm, and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cubic cm of wood has a mass of 0.6 gm.

The correct answer is: The mass of the pipe is 3432 gm.


    The wooden pipe is hollow inside. So, we have to calculate its width volume, by subtracting the volume with inner radius from the volume with outer radius. Then, we multiply the given mass for 1 cubic cm of wood with the calculated area to get the total mass of the pipe.
    We take  = pi 22/7.
    Step 1 of 3:
    The inner diameter of a cylindrical wooden pipe is 24 cm. So, the inner radius is r subscript i equals 24 over 2 equals12 cm.
    The outer diameter of a cylindrical wooden pipe is 24 cm. So, the outer radius is  r subscript 0 equals 28 over 2 equals14 cm.
    Step 2 of 3:
    We know that, if the radius of a cylinder is r and height be h, then the volume is pi r squared h .
    Now, the volume of the wood only is pi r subscript o superscript 2 h minus pi r subscript i superscript 2 h
    equals pi h open parentheses r subscript o superscript 2 minus r subscript i superscript 2 close parentheses
    equals 22 over 7 cross times 35 cross times open parentheses 14 squared minus 12 squared close parentheses
    equals 22 over 7 cross times 35 cross times left parenthesis 14 plus 12 right parenthesis cross times left parenthesis 14 minus 12 right parenthesis comma open square brackets a squared minus b squared equals left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis close square brackets
    equals 22 over 7 cross times 35 cross times 26 cross times 2
    equals 5720 cm cubed
    Step 3 of 3:
    It is given that 1 cubic cm of wood has a mass of 0.6 gm.
    therefore 5720 cm3 of wood would have a mass of 5720 cross times 0.6 equals 3432gm
    Final Answer:
    The mass of the pipe is 3432 gm.
     

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