A cylindrical storage silo has a radius of 5 meters and a height of 12 meters. The silo needs to be painted on its top and curved side, but not the bottom. If one liter of paint covers 10 square meters, how many liters of paint are needed to paint the silo, rounded up to the nearest whole liter? (Use π ≈ 3.14)
- A38 liters
- B46 liters
- C60 liters
- D53 liters
Show answer & explanationAnswer & explanation
Correct answer: B. 46 liters
The area to be painted includes the top circle and the lateral surface area. 1. Area of the top circle (A_top) = πr² = 3.14 * (5)² = 3.14 * 25 = 78.5 square meters. 2. Lateral surface area (A_lateral) = 2πrh = 2 * 3.14 * 5 * 12 = 3.14 * 120 = 376.8 square meters. 3. Total area to paint = A_top + A_lateral = 78.5 + 376.8 = 455.3 square meters. 4. Liters of paint needed = Total area / Coverage per liter = 455.3 / 10 = 45.53 liters. 5. Rounded up to the nearest whole liter, 46 liters are needed.
Why the other options are wrong
- A. This would be the result if only the lateral surface area was used, and then rounded down, or a calculation error.
- C. This would be a significant overestimation or a calculation error, possibly including both top and bottom areas.
- D. This might be the result if the bottom area was also included, or a calculation error.
Surface Area of a Cylinder (Partial)
Calculating the surface area of a cylinder often involves summing the areas of its circular bases (top and bottom) and its lateral (curved) surface, adapting for specific painting/covering needs.
- Lateral Surface Area: 2πrh
- Area of one circular base: πr²
- Total Surface Area: 2πr² + 2πrh
- For top and lateral only: πr² + 2πrh
Memory trick: Top circle, curved side, sum them up, then divide!