Final answer:
To find the width of a wall given its volume and that its height is six times its width and length is seven times its height, we use the volume formula for rectangular prisms. After setting up the equation with the given proportions and volume, we solve for the width and find that it is 4 meters.
Step-by-step explanation:
We are given that the height of a wall is six times its width and the length of the wall is seven times its height, and we need to find the wall's width given that its volume is 16128 cubic meters. Let us denote the width of the wall as w, the height as 6w, and the length as 42w (since it's seven times the height which is already in terms of width).
Using the formula for the volume of a rectangular prism, which is volume = length x width x height, we can set up the equation using the given volumes and proportions:
16128 cu. m = 42w x w x 6w
This simplifies to:
16128 = 252w³
Dividing both sides by 252 to solve for w³ gives:
w³ = 16128 / 252
w³ = 64
Since w³ is a perfect cube, we can take the cube root of both sides to find:
w = √³64
w = 4 meters
Therefore, the width of the wall is 4 meters.