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.
__ in.^2
First, we need to calculate the surface area of the rain barrel.
The rain barrel consists of three main surfaces: the top and bottom circles, and the side (or lateral) surface.
1. Top and bottom circles:
The formula to calculate the area of a circle is A = πr^2, where r is the radius of the circle. Since the diameter of the rain barrel is 24 inches, the radius is half of that, which is 12 inches.
Area of a circle = 3.14 x 12^2 = 3.14 x 144 = 452.16 in^2
Since there are two circles (top and bottom), the total area for the circles is: 2 x 452.16 = 904.32 in^2
2. Lateral (or side) surface:
The lateral surface area of a cylinder can be calculated by the formula A = 2Ï€rh, where r is the radius and h is the height of the cylinder.
Lateral surface area = 2 x 3.14 x 12 x 48 = 3.14 x 24 x 48 = 3.14 x 1152 = 3612.48 in^2
3. Total surface area:
Total surface area = Area of circles + Lateral surface area
Total surface area = 904.32 + 3612.48 = 4516.8 in^2
Therefore, the surface area of the rain barrel is 4516.8 square inches. Rounded to the nearest tenth, it is 4516.8 in^2.