# Use a triple integral to find the volume of the solid in the first octant bounded by the...

## Question:

Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate planes and the plane 45x + 90y +8z =720.

## Volume of a Tetrahedron:

Integration can be used to find the volume of a solid. With the given equation, we can find the value of z and then double integrate it to find the volume with limits of {eq}x,y {/eq}. The volume is given by the formula {eq}V=\int \int z dydx {/eq}

First, we'll write the plane equation in terms of z:

{eq}\displaystyle 45x+90y+8z = 720 {/eq}

{eq}\displaystyle...

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