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.
First, we need to calculate the lateral surface area of the rain barrel, which is the combined area of the two circular ends.
The formula for the lateral surface area of a cylinder is 2πrh.
Plugging in the values:
2 * 3.14 * 24 * 48 = 7,257.6 square inches
Next, we need to calculate the surface area of the two circular ends of the rain barrel, which is the area of one circle.
The formula for the area of a circle is πr^2.
Plugging in the radius (which is half the diameter): 24 / 2 = 12
3.14 * 12^2 = 452.16 square inches
Now, to find the total surface area of the rain barrel, we add the lateral surface area to the area of the two circular ends:
7,257.6 + 452.16 + 452.16 = 8,161.9 square inches
Therefore, the surface area of the rain barrel is 8,161.9 square inches.
wrong
I apologize for the error in my previous response. Let me correct the calculation.
The lateral surface area of a cylinder is given by:
Lateral surface area = 2πrh
where r is the radius and h is the height of the cylinder.
Given that the diameter of the rain barrel is 24 inches, the radius is 24 / 2 = 12 inches.
Plugging in the values:
Lateral surface area = 2 * 3.14 * 12 * 48 = 3,442.56 square inches
Next, we need to calculate the surface area of the two circular ends of the rain barrel:
The area of one circular end = πr^2
Plugging in the radius: 3.14 * 12^2 = 452.16 square inches
Since there are two circular ends, the total surface area of the circular ends is 2 * 452.16 = 904.32 square inches
Adding the lateral surface area and the area of the two circular ends:
3,442.56 + 904.32 = 4,346.88 square inches
Therefore, the correct surface area of the rain barrel is 4,346.88 square inches.