surface area of cylinders practice find the surface area of a cylinder with a diameter of 12 inches and a height of 10 inches use the approximation for 3.14 for pi
To find the surface area (A) of a cylinder, we need to calculate the area of the two bases and the lateral surface area.
1. The area of each base can be found using the formula for the area of a circle: A_base = π * r^2, where r is the radius of the base. We are given the diameter (d) of 12 inches, so the radius (r) is half of that: r = d/2 = 12/2 = 6 inches. Therefore, A_base = 3.14 * (6)^2 = 3.14 * 36 = 113.04 square inches.
2. The lateral surface area of a cylinder can be found using the formula: A_lateral = 2πrh, where r is the radius of the base and h is the height of the cylinder. In this case, r = 6 inches and h = 10 inches. Therefore, A_lateral = 2 * 3.14 * 6 * 10 = 376.8 square inches.
3. Finally, we can calculate the total surface area by summing the area of the two bases and the lateral surface area: A = 2A_base + A_lateral = 2 * 113.04 + 376.8 = 339.68 + 376.8 = 716.48 square inches (approximated to two decimal places).
Therefore, the surface area of the given cylinder is approximately 716.48 square inches.