Find the volume of the indicated region.
-the region in the first octant bounded by the coordinate planes and the planes x + z = 9, y + 4z = 36
A) 4374
B) 54
C) 486
D) $\frac { 243 } { 2 }$

Question

Find the volume of the indicated region.
-the region in the first octant bounded by the coordinate planes and the planes x + z = 9, y + 4z = 36 
A) 4374
B) 54
C) 486
D) $\frac { 243 } { 2 }$

Quizplus · Accepted Answer

Solving both the equations for z, we get z = 9 - x and z = (36 - y)/4. Since the region is in the first octant, we can set up the integral as follows:

$$\int_{0}^{9}\int_{0}^{36-4z}\int_{0}^{9-x}\,dx\,dy\,dz$$

Evaluating the integral, we get the volume as 486.

Find the Volume of the Indicated Region 2432\frac { 243 } { 2 }2243​

Find the Volume of the Indicated Region $\frac { 243 } { 2 }$