Joseph has a rain barrel in the shape of a cylinder with a height of 48 inches and a diameter of 24 inches. What is the surface area of the rain barrel? Use 3.14
To find the surface area of the rain barrel, we need to find the lateral surface area of the cylinder plus the area of the two circular bases.
The lateral surface area of a cylinder can be calculated using the formula:
Lateral Surface Area = 2 * π * r * h
where r is the radius of the cylinder and h is the height of the cylinder.
Given that the diameter of the cylinder is 24 inches, the radius (r) is half of the diameter, so r = 24 / 2 = 12 inches.
Plugging in the values, we get:
Lateral Surface Area = 2 * 3.14 * 12 * 48
Lateral Surface Area = 3619.52 square inches
The area of the two circular bases can be calculated using the formula for the area of a circle:
Base Area = π * r^2
Plugging in the values, we get:
Base Area = 3.14 * 12^2
Base Area = 3.14 * 144
Base Area = 452.16 square inches
Therefore, the total surface area of the rain barrel is the sum of the lateral surface area and the base area:
Total Surface Area = Lateral Surface Area + 2 * Base Area
Total Surface Area = 3619.52 + 2 * 452.16
Total Surface Area = 4523.84 square inches
Therefore, the surface area of the rain barrel is 4523.84 square inches.