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Thread: Find the volume of the given solid. Bounded by the coordinate planes and the plane

  1. #1
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    Find the volume of the given solid. Bounded by the coordinate planes and the plane

    Find the volume of the given solid.Bounded by the coordinate planes and the plane: 5x + 3y + z = 15



    I do not know where I am going wrong. I found the intercepts, used point slope and integrated. My solution - 369/2 - is incorrect. any help?
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  2. #2
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    Re: Find the volume of the given solid. Bounded by the coordinate planes and the plan

    well let's take a look.

    at $z=0$ this reduces to

    $5x + 3y = 15$

    $y = 5 - \dfrac 5 3 x$

    and as we are also bounded by $y=0$ we note that this occurs at $x=3$

    so we integrate

    $\displaystyle \int_0^3 \int_0^{5-\frac 5 3 x}\int_0^{15-5x-3y}~dz~dy~dx = \dfrac{75}{2}$
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