Tanks A and B are each in the shape of a right circular cylinder. The interior…
2025
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
- A.
a is 80% of b
- B.
b is 18% of a
- C.
b is 80% of a
- D.
a is 18% of b
Show answer & explanation
Correct answer: A
A right circular cylinder's volume is V = πr2h, where r is the radius and h is the height. Since the circumference is C = 2πr, the radius is directly proportional to the circumference: r = C / (2π). So for two cylinders, the ratio of their volumes equals the square of the ratio of their circumferences, multiplied by the ratio of their heights: VA/VB = (CA/CB)2 × (hA/hB).
Radius of tank A: rA = CA / (2π) = 8 / (2π) = 4/π metres.
Radius of tank B: rB = CB / (2π) = 10 / (2π) = 5/π metres.
Volume of tank A: VA = πrA2hA = π × (4/π)2 × 10 = 160/π cubic metres.
Volume of tank B: VB = πrB2hB = π × (5/π)2 × 8 = 200/π cubic metres.
Ratio: VA/VB = (160/π) / (200/π) = 160/200 = 0.8 = 80%.
Cross-check with the shortcut ratio formula, avoiding the π terms entirely: (CA/CB)2 × (hA/hB) = (8/10)2 × (10/8) = 0.64 × 1.25 = 0.8, which matches the full computation exactly.
Therefore, the capacity of tank A is 80% of the capacity of tank B.