Tank depth from base area and volume (unit conversion care): A rectangular tank has base area 6500 cm^2 and holds 2.6 m^3 of water. Find the depth (in meters).

Introduction / Context:This item checks careful unit conversion between cm^2 and m^2 before applying depth = volume / area. Mismatched units are a common trap.

Given Data / Assumptions:

• A_base = 6500 cm^2 = 0.65 m^2 (since 1 m^2 = 10,000 cm^2)
• V = 2.6 m^3
• Depth d = V / A_base

Concept / Approach:Convert the base area to m^2, then divide the volume by this area to get meters for depth.

Step-by-Step Solution:A_base = 6500 / 10000 = 0.65 m^2d = 2.6 / 0.65 = 4 m

Verification / Alternative check:Back-check: 0.65 m^2 * 4 m = 2.6 m^3—exactly the stated volume.

Why Other Options Are Wrong:3.5 m and 5 m are off due to unit slips; 8 m doubles the correct value; 2 m halves it.

Common Pitfalls:Converting cm^2 as if it were a linear unit; dividing 2.6 by 6500 (forgetting to convert area units first).

Final Answer:4 m