Sheet thickness from volume and spread area: Half a cubic meter of gold is hammered into a sheet that covers 1 hectare. Find the sheet’s thickness in cm.

Introduction / Context:Volume conservation gives thickness when a volume is spread uniformly over a known area. This tests conversions between meters and centimeters and hectares to square meters.

Given Data / Assumptions:

• Volume V = 0.5 m^3
• Area A = 1 hectare = 10,000 m^2
• Thickness t = V / A (in meters), then convert to centimeters

Concept / Approach:Use t = V / A. Convert meters to centimeters by multiplying by 100 (1 m = 100 cm).

Step-by-Step Solution:t (in m) = 0.5 / 10000 = 0.00005 mt (in cm) = 0.00005 * 100 = 0.005 cm

Verification / Alternative check:Back-check: Area * thickness = 10,000 m^2 * 0.00005 m = 0.5 m^3, confirming consistency.

Why Other Options Are Wrong:0.5 cm and 0.05 cm are 100× and 10× too thick; 0.0005 cm and 0.00005 cm are 10× and 100× too thin.

Common Pitfalls:Confusing cm with m; using 1 hectare = 1000 m^2 (incorrect); forgetting to multiply by 100 when converting thickness to cm.

Final Answer:0.005 cm