Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate planes, usi

Question

3 years ago

8

ng triple integrals.

1 answer:

dem82 [27] · Answer 1 · 2022-08-25T08:50:31+03:00

dem82 [27]3 years ago

3 0

First,

$9x+15y+15z=45\implies 3x+5y+5z=15$

The volume is given by the integral (one of 6 possible combinations),

$\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}$

Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate​ planes, usi