Martha has a soup can in the shape of a cylinder with a height of 11 cm and radius of 4 cm. What is the surface area of the can? Use 3.14 for π and round to the nearest tenth.(1 point)
I apologize for the mistake in my previous responses. Let's correct it once again.
Given:
Height (h) = 11 cm
Radius (r) = 4 cm
Surface Area of a cylinder consists of three parts:
1. Two circular bases
2. Lateral surface area
1. Area of two circular bases:
Area = 2 * π * r²
Area = 2 * 3.14 * 4²
Area = 2 * 3.14 * 16
Area = 2 * 50.24
Area = 100.48 cm²
2. Lateral surface area:
Lateral surface area = 2 * π * r * h
Lateral surface area = 2 * 3.14 * 4 * 11
Lateral surface area = 2 * 3.14 * 44
Lateral surface area = 2 * 138.16
Lateral surface area = 276.32 cm²
Total surface area:
Total surface area = 100.48 + 276.32
Total surface area = 376.8 cm²
Therefore, the total surface area of the soup can is 376.8 cm². Thank you for your patience, and I hope this clarifies it.
To find the surface area of the can, we need to calculate the area of the side (lateral surface area) and the area of the two circular bases.
Lateral Surface Area:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2(3.14)(4)(11)
Lateral Surface Area = 8(3.14)(11)
Lateral Surface Area = 87.92 cm²
Circular Base Area:
The area of one circular base = πr²
Area of one circular base = 3.14(4)²
Area of one circular base = 3.14(16)
Area of one circular base = 50.24 cm²
Since the can has two circular bases, the total area of both bases is:
Total base area = 2(50.24)
Total base area = 100.48 cm²
Now, to find the total surface area of the can, we add the lateral surface area and the total base area:
Total surface area = Lateral Surface Area + Total Base Area
Total surface area = 87.92 + 100.48
Total surface area = 188.4 cm²
Therefore, the surface area of the soup can is approximately 188.4 cm².
thats wrong
I apologize for the error in my previous response. Let's correct it:
The lateral surface area of a cylinder is given by the formula:
Lateral Surface Area = 2πrh
where:
r = radius = 4 cm
h = height = 11 cm
Let's calculate the lateral surface area:
Lateral Surface Area = 2(3.14)(4)(11)
Lateral Surface Area = 8(3.14)(11)
Lateral Surface Area = 88(3.14)
Lateral Surface Area = 276.32 cm²
Next, we need to calculate the area of the two circular bases:
Circular Base Area = πr²
Circular Base Area = 3.14(4)²
Circular Base Area = 3.14(16)
Circular Base Area = 50.24 cm²
Since there are two circular bases, the total area of both bases is:
Total Base Area = 2(50.24)
Total Base Area = 100.48 cm²
Now, to find the total surface area of the can:
Total Surface Area = Lateral Surface Area + Total Base Area
Total Surface Area = 276.32 + 100.48
Total Surface Area = 376.8 cm²
Therefore, the corrected total surface area of the soup can is approximately 376.8 cm².