Question
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
Answers
GPT 3.5
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.
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.