What is the internal surface area, in square feet, of a cylindrical tank with a diameter of 65.0 ft and a height of 24.0 ft, assuming the top is flat?

What is the internal surface area, in square feet, of a cylindrical tank with a diameter of 65.0 ft and a height of 24.0 ft, assuming the top is flat?

• A. 10,000 ft^2
• B. 11,531.65 ft^2
• C. 9,500 ft^2
• D. 12,000 ft^2

Answer: (B)

Internal surface area of a closed cylinder includes the curved side and both flat ends. Start with the radius, which is half the diameter: r = 32.5 ft, and the height is 24 ft. The lateral surface area is 2πrh = 2π × 32.5 × 24 = 1560π ft^2. The areas of the two ends are 2πr^2 = 2π × (32.5)^2 = 2112.5π ft^2. Adding these gives total internal surface area = (1560π + 2112.5π) = 3672.5π ft^2. Using π ≈ 3.14, this is 3672.5 × 3.14 ≈ 11,531.65 ft^2. The top being flat means the tank is closed, so you include the top circular area as part of the interior surface. If you used a more precise π, you’d get about 11,537.5 ft^2, but the rounding with 3.14 matches the given value.

Internal surface area of a closed cylinder includes the curved side and both flat ends. Start with the radius, which is half the diameter: r = 32.5 ft, and the height is 24 ft. The lateral surface area is 2πrh = 2π × 32.5 × 24 = 1560π ft^2. The areas of the two ends are 2πr^2 = 2π × (32.5)^2 = 2112.5π ft^2. Adding these gives total internal surface area = (1560π + 2112.5π) = 3672.5π ft^2. Using π ≈ 3.14, this is 3672.5 × 3.14 ≈ 11,531.65 ft^2. The top being flat means the tank is closed, so you include the top circular area as part of the interior surface. If you used a more precise π, you’d get about 11,537.5 ft^2, but the rounding with 3.14 matches the given value.