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 for π and round to the nearest tenth.?.
To find the surface area of the rain barrel, we need to calculate the areas of the two circular ends and the lateral surface area of the cylinder.
1. Area of the two circular ends:
Each end is a circle with a diameter of 24 inches, so the radius is half of the diameter, which is 12 inches.
Area of one circular end = π * r^2
Area = 3.14 * (12)^2
Area = 3.14 * 144
Area = 452.16 square inches
Since there are two circular ends, the total area of both ends is:
Total area of ends = 2 * 452.16
Total area of ends = 904.32 square inches
2. Lateral surface area of the cylinder:
The lateral surface area of a cylinder is given by the formula:
Lateral surface area = 2 * π * r * h
where r is the radius and h is the height.
Radius, r = 12 inches
Height, h = 48 inches
Lateral surface area = 2 * 3.14 * 12 * 48
Lateral surface area = 2 * 3.14 * 576
Lateral surface area = 2 * 1809.6
Lateral surface area = 3619.2 square inches
3. Total surface area of the rain barrel:
Total surface area = Total area of ends + Lateral surface area
Total surface area = 904.32 + 3619.2
Total surface area = 4523.5 square inches
Therefore, the surface area of the rain barrel is approximately 4523.5 square inches.