Solve the problem.
-Solve for a:
$$\int _ { a } ^ { 9 a } \int _ { a } ^ { 9 a } \int _ { a } ^ { 9 a } d x d z d y = 512$$
A) $a = 1$
B) $a = 2$
C) $a = \frac { 8 } { 5 }$
D) $a = \frac { 4 } { 5 }$

Question

Quizplus · Accepted Answer

When we integrate over the bounds of x, y, and z, we get the volume of a cube with side length 8a. Therefore, the volume is $(8a)^3=512a^3$. Setting this equal to 512 and solving for a, we get a=1. Therefore, the answer is A.

Solve the Problem ∫a9a∫a9a∫a9adxdzdy=512\int _ { a } ^ { 9 a } \int _ { a } ^ { 9 a } \int _ { a } ^ { 9 a } d x d z d y = 512∫a9a​∫a9a​∫a9a​dxdzdy=512

Solve the Problem $\int _ { a } ^ { 9 a } \int _ { a } ^ { 9 a } \int _ { a } ^ { 9 a } d x d z d y = 512$