Find breadth from wall volume relation: A wall is 5 times as high as it is broad and 8 times as long as it is high. If its volume is 12.8 m3, find the breadth (in cm).

Introduction / Context:
The wall’s three dimensions are given in chained ratios in terms of breadth b. Express height and length in b, form the volume equation, and solve for b. Finally convert meters to centimeters.

Given Data / Assumptions:

• Breadth = b, Height = 5b, Length = 8*(Height) = 40b
• Volume = 12.8 m3

Concept / Approach:

• Volume V = b * 5b * 40b = 200 b^3.
• Solve for b^3 = V / 200, then take cube root.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 22.5/25/30 cm: Do not satisfy 200 b^3 = 12.8 when converted back.

Common Pitfalls:

• Using 8 times the breadth instead of 8 times the height for length.
• Incorrect meter–centimeter conversion.

Final Answer:

40 cm