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Math Help - Finding the volume

  1. #1
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    Exclamation Finding the volume

    A circular concrete conduit, whose inside diameter is 10 ft., is 1 ft. thick. It rises 16 ft. per 1000 horizontal feet. The vertical plane which contains the axis is perpendicular to the two vertical planes which contain the ends of the conduit. If the ends are 3000 ft. apart, find the amount of concrete used in the construction of the conduit.

    Help me solve this problem.
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  2. #2
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    Quote Originally Posted by jasonlewiz View Post
    A circular concrete conduit, whose inside diameter is 10 ft., is 1 ft. thick. It rises 16 ft. per 1000 horizontal feet. The vertical plane which contains the axis is perpendicular to the two vertical planes which contain the ends of the conduit. If the ends are 3000 ft. apart, find the amount of concrete used in the construction of the conduit.

    Help me solve this problem.
    First find the length of the conduit, using the Pythagorean theorem: vertically, it is 3000 feet long and,since it rises 16 feet per 1000 horizontal feet, it rises 3(16)= 48. The conduit itself is the hypotenuse of a right triangle with legs of length 3000 and 48- its length is [tex]\sqrt{3000^2+ 48^2}.

    Now think of the cross section as two circles. The inner circle has radius 10 and the outer circle has radius 1. Find the areas of those two circles and subtract to find the area between them. Multiply that area by the length of the conduit.
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  3. #3
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    Hello, jasonlewiz!

    A circular concrete conduit, whose inside diameter is 10 ft., is 1 ft. thick.
    It rises 16 ft. per 1000 horizontal feet.
    The vertical plane which contains the axis is perpendicular to
    the two vertical planes which contain the ends of the conduit.
    If the ends are 3000 ft. apart, find the amount of concrete used in the conduit.

    Theat"vertical plane" decription is confusing.
    If I read it correctly, it means that the circular ends of the cylinder
    . . are perpendicular to the axis of the cylinder.
    That is, we have a right circular cylinder (which happens to be tipped).

    We have an outer cylinder with radius 6 and height 3000.
    . . Its volume is: . \pi (6^2)(3000 \:=\:108,000\pi\text{ ft}^3.

    We have an inner cylinder with radius 5 and height 3000.
    . . Its volume if: . \pi(5^2)(3000) \:=\:75,000\pi\text{ ft}^3.

    Therefore, the volume of the concrete is: . 108,000\pi - 75,000\pi \;=\; 33,000\pi\text{ ft}^3.

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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    First find the length of the conduit, using the Pythagorean theorem: vertically, it is 3000 feet long and,since it rises 16 feet per 1000 horizontal feet, it rises 3(16)= 48. The conduit itself is the hypotenuse of a right triangle with legs of length 3000 and 48- its length is [tex]\sqrt{3000^2+ 48^2}.

    Now think of the cross section as two circles. The inner circle has radius 10 and the outer circle has radius 1. Find the areas of those two circles and subtract to find the area between them. Multiply that area by the length of the conduit.
    This is the right solution. I try it ^^
    Last edited by jasonlewiz; January 25th 2010 at 02:28 AM.
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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, jasonlewiz!


    Theat"vertical plane" decription is confusing.
    If I read it correctly, it means that the circular ends of the cylinder
    . . are perpendicular to the axis of the cylinder.
    That is, we have a right circular cylinder (which happens to be tipped).

    We have an outer cylinder with radius 6 and height 3000.
    . . Its volume is: . \pi (6^2)(3000 \:=\:108,000\pi\text{ ft}^3.

    We have an inner cylinder with radius 5 and height 3000.
    . . Its volume if: . \pi(5^2)(3000) \:=\:75,000\pi\text{ ft}^3.

    Therefore, the volume of the concrete is: . 108,000\pi - 75,000\pi \;=\; 33,000\pi\text{ ft}^3.


    Sir, I try your solution and the answer is 103,672.56 cu.ft.

    But the answer in my book is 103,690 cu. ft. it is close ^^
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