Cuboid dimensions from surface area and ratio: A cuboid has length : breadth : height in the ratio 6 : 5 : 4. If its total surface area is 33,300 cm2, find the actual dimensions (in cm) of length, breadth, and height.

Introduction / Context:We are given the ratio of the edges of a cuboid and its total surface area (TSA). Using the TSA formula and ratio scaling, we can determine the exact dimensions. This tests ratio scaling with geometric surface area.

Given Data / Assumptions:

• Edge ratio: l : b : h = 6 : 5 : 4
• Total surface area (TSA) = 33,300 cm2
• Let l = 6k, b = 5k, h = 4k for some k > 0

Concept / Approach:

• Cuboid TSA = 2 * (l*b + b*h + h*l)
• Substitute proportional edges, solve for k, then compute actual dimensions.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 90, 85, 60: Breaks the ratio 6 : 5 : 4.
• 85, 75, 60: Not in a constant multiple of 6 : 5 : 4.
• 90, 75, 70: Violates the 4-part for height.

Common Pitfalls:

• Forgetting to multiply all three pairwise products inside TSA.
• Using perimeter-like formula instead of surface area.
• Taking k = √(33300/148) but rounding incorrectly; here it is exactly 15.

Final Answer:

90, 75, 60