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

1. 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?

2. 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

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