Square the inner radius, then multiply the product by pi to find the area of an end ring's inner circle. For this example, let the inner radius measure 2 inches. The square of 2 inches is 4 squared inches, and 4 square inches multiplied by pi results in approximately 12.57 square inches.
Square the outer radius, then multiply the product by pi to find the area of an end ring's outer circle. For this example, let the outer radius measure 4 inches to find the area of the outer circle. The square of 4 inches is 16 square inches, and 16 square inches multiplied by pi results in approximately 50.27 square inches.
Subtract the inner circle's area from the outer circle's area and multiply the difference by 2 to calculate the surface area of the two end rings — 50.27 square inches less 12.57 square inches results in 37.7 square inches, and 37.7 square inches multiplied by 2 equals 75.4 square inches.
Multiply the inner radius by pi — 2 inches multiplied by pi approximately equals 6.28 inches.
Multiply the product of the inner radius and pi by the cylinder's height. For this example, let the height be 5 inches — 6.28 inches multiplied by 5 inches equals 31.4 square inches.
Double the product of the inner radius, pi and height to find the inner curved surface area — 31.4 square inches multiplied by 2 equals 62.8 square inches.
Multiply the outer radius by pi — 4 inches multiplied by pi approximately equals 12.57 inches.
Multiply the product of the outer radius and pi by the cylinder's height, then double the product to calculate the outer curved surface area — 12.57 inches multiplied by 5 inches 62.85 square inches, which becomes 125.7 square inches when doubled.
Add the areas of the two circular ends and the inner and outer curved surface areas together to calculate the cylinder's total surface area — adding together 75.4, 62.8 and 125.7 square inches equals 263.9 square inches.