The cylinder's surface area is approximately 200 square feet, calculated by summing the lateral surface area and the total base area. Rounding to the nearest thousand, the result is 200 square feet.
The Cylinder's Surface Area:
1. Identify the formula and values:
Formula: 2πrh + 2πr² (where r is the radius and h is the height)
Radius (r): 3 feet
Height (h): 8 feet
2. Calculate the lateral surface area:
Lateral surface area = 2πrh
Substitute the values: 2π(3)(8) = 48π square feet
3. Calculate the area of one circular base:
Area of a circle = πr²
Substitute the value: π(3)² = 9π square feet
4. Calculate the total area of both bases:
Total base area = 2 * 9π = 18π square feet
5. Combine the lateral and base areas to find the total surface area:
Total surface area = lateral area + base area
Substitute the calculated values: 48π + 18π = 66π square feet
6. Round the answer to the nearest thousand:
66π ≈ 207 square feet
Rounding to the nearest thousand: 207 ≈ 200 square feet
Therefore, the approximate surface area of the cylinder is 200 square feet.