The surface area of a cylinder is calculated by adding the area of the two circular bases and the lateral surface area.
First, let's calculate the area of the two circular bases:
Radius = diameter/2 = 24/2 = 12 inches
Base area = π*radius^2 = 3.14*12^2 = 452.16 square inches
Now, let's calculate the lateral surface area:
Lateral surface area = height * circumference of the base
Circumference = 2*π*radius = 2*3.14*12 = 75.36 inches
Lateral surface area = 48*75.36 = 3,620.88 square inches
Now, let's total up the surface area:
Total surface area = 2*Base area + Lateral surface area
Total surface area = 2*452.16 + 3,620.88
Total surface area = 904.32 + 3,620.88
Total surface area = 4,525.2 square inches
Rounded to the nearest tenth, the surface area of the rain barrel is 4,525.2 in^2.