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Math Help - Volume of half a cyclindar

  1. #1
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    Volume of half a cyclindar

    I have a cyclindar that is 7 m high, 14 meters in diameter, and 7 m wide. I need to use a definite integral to determine the volume of this taking slices from the bottom to the top of it. So, I need to evalute the integral from 0 to 7 of pi (7-h)2 and since it is only half a cyclindar I would multiple the whole integral by 1/2. Am I close to right here???? THis is the most confusing assignment I have come up against and I do not have a way to check if I am doing this correctly. Thanks for the assistance all you smart math folks.
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  2. #2
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    You're just using integration to find the volume of the cylinder with radius 7 and height 7?.

    Using the equation of the base, which is a circle of radius 7.

    x^{2}+y^{2}=49

    7\int_{-7}^{7}\sqrt{49-x^{2}}dx
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  3. #3
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    Cylinder volume

    Actually, I misspoke. The cylinder has a radius of 7, is 7 units tall but it is 10 units in depth in other words I need to take slices from 0 to 7 units in height but I have to account for it being 10 units in thickness. I only go from 0 to 7 since I have half a cylinder. If I had a whole cylinder I would go from -7 to 7 correct? So, my integral would be from 0 to 7 of pi times radius squared but how do I account for the 10 units of depth????
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  4. #4
    Eater of Worlds
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    I'm confused about what you mean. A cylinder has a radius and a height.

    Thus we have the formula for volume of a cylinder. {\pi}r^{2}h

    When you compute your integral, compare it to that formula.

    What do you mean by thickness?. I am thinking the cylinder has a 7 inch radius(14 inch diameter) and is 10 inches tall?.

    If that is the case, just use the integral I gave. To incorporate the height just multiply by it.
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