To determine the surface area of a cylinder, we first need to calculate the area of the circular base using the formula for the area of a circle: A = πr^2. Given that the diameter is 10, the radius (r) is half of that, so r = 5.
1. Area of the circular base:
A = π(5)^2 = 25π ≈ 78.54 square inches
Next, we need to calculate the width of the lateral face of the cylinder, which is the same as the circumference of the circular base. The formula for the circumference of a circle is C = 2πr.
2. Width of the lateral face:
C = 2π(5) = 10π ≈ 31.41 inches
To find the area of the lateral face, we need to multiply the width by the height of the cylinder:
3. Area of the lateral face:
31.41 * 3 = 94.23 square inches
Finally, to calculate the total surface area of the cylinder, we add the area of the circular base and the area of the lateral face (including the top and bottom faces):
4. Total surface area:
78.54 + 94.23 = 172.77 square inches
Therefore, the total surface area of the cylinder is approximately 172.77 square inches.