Tanks A and B are right circular cylinders with different heights and circumferences. Tank A has interior height 10 m and interior circumference 8 m, and tank B has interior height 8 m and interior circumference 10 m. If both tanks are completely full, the capacity (volume) of tank A is what percentage of the capacity of tank B?

Introduction / Context:
This question compares the capacities of two cylindrical tanks when their heights and circumferences are interchanged. It tests understanding of how the volume of a cylinder depends on its radius and height, and how to express one volume as a percentage of another.

Given Data / Assumptions:

• Tank A is a right circular cylinder with height 10 m and interior circumference 8 m.
• Tank B is a right circular cylinder with height 8 m and interior circumference 10 m.
• Both tanks are considered completely full when comparing volumes.
• Volumes are compared using exact geometric formulas, and the percentage is rounded as a simple ratio.

Concept / Approach:
The volume of a right circular cylinder is given by V = π * r^2 * h, where r is the radius and h is the height. The circumference of a circle is C = 2 * π * r. From the circumference we can find r, and then substitute into the volume formula. Because π will cancel when forming the ratio, we can work directly with C and h to compare the two capacities.

Step-by-Step Solution:
Step 1: Use C = 2 * π * r so r = C / (2 * π). Step 2: Substitute r into V = π * r^2 * h to get V = (C^2 * h) / (4 * π). Step 3: For tank A: C = 8 m, h = 10 m, so V_A is proportional to 8^2 * 10 = 64 * 10 = 640. Step 4: For tank B: C = 10 m, h = 8 m, so V_B is proportional to 10^2 * 8 = 100 * 8 = 800. Step 5: Ratio V_A : V_B = 640 : 800 = 64 : 80 = 4 : 5. Step 6: Therefore V_A is (4 / 5) * 100% = 80% of V_B.

Verification / Alternative check:
Instead of writing the full formula, one can directly use the proportional relation V is proportional to C^2 * h. Plugging the same values again gives 640 for tank A and 800 for tank B, confirming that the fraction is 640 / 800 = 0.8, which is 80%.

Why Other Options Are Wrong:

• 76% and 72% are lower than the correct ratio 80% and do not match the computed fraction 640 / 800.
• 82% is close to 80% but still does not equal the exact ratio 4 / 5.

Common Pitfalls:
A frequent mistake is to compare only heights or only circumferences instead of using both together. Another common error is forgetting that volume depends on the square of the radius, which means it depends on the square of the circumference. Ignoring this square leads to wrong ratios. Being systematic with the formulas avoids such errors.

Final Answer:
The capacity of tank A is 80% of the capacity of tank B.