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Answer :
To find the minimum amount of plastic wrap needed to completely wrap 8 cylindrical containers, we need to calculate the surface area of one container and then multiply it by 8. Here's how you can do it:
1. Find the Radius:
- The diameter of each cylindrical container is 5.5 inches.
- The radius is half the diameter, so the radius is [tex]\( \frac{5.5}{2} = 2.75 \)[/tex] inches.
2. Calculate the Surface Area of One Container:
- Lateral Surface Area: This is the area around the side of the cylinder. The formula is [tex]\( 2\pi \times \text{radius} \times \text{height} \)[/tex].
- Plug in the values: [tex]\( 2 \times 3.14 \times 2.75 \times 3 = 51.8 \)[/tex] square inches.
- Top and Bottom Area: Each cylinder has two circular ends. The formula for the area of a circle is [tex]\( \pi \times \text{radius}^2 \)[/tex].
- So, the area of one end is [tex]\( 3.14 \times 2.75^2 = 23.7 \)[/tex] square inches.
- Since there are two ends, multiply this by 2: [tex]\( 2 \times 23.7 = 47.4 \)[/tex] square inches.
- Total Surface Area for One Container: Add the lateral area and the top and bottom areas together.
- Total surface area = [tex]\( 51.8 + 47.4 = 99.3 \)[/tex] square inches.
3. Calculate the Total Surface Area for 8 Containers:
- Multiply the surface area of one container by 8: [tex]\( 99.3 \times 8 = 794.4 \)[/tex] square inches.
Therefore, the minimum amount of plastic wrap needed to completely wrap 8 containers is 794.4 square inches.
1. Find the Radius:
- The diameter of each cylindrical container is 5.5 inches.
- The radius is half the diameter, so the radius is [tex]\( \frac{5.5}{2} = 2.75 \)[/tex] inches.
2. Calculate the Surface Area of One Container:
- Lateral Surface Area: This is the area around the side of the cylinder. The formula is [tex]\( 2\pi \times \text{radius} \times \text{height} \)[/tex].
- Plug in the values: [tex]\( 2 \times 3.14 \times 2.75 \times 3 = 51.8 \)[/tex] square inches.
- Top and Bottom Area: Each cylinder has two circular ends. The formula for the area of a circle is [tex]\( \pi \times \text{radius}^2 \)[/tex].
- So, the area of one end is [tex]\( 3.14 \times 2.75^2 = 23.7 \)[/tex] square inches.
- Since there are two ends, multiply this by 2: [tex]\( 2 \times 23.7 = 47.4 \)[/tex] square inches.
- Total Surface Area for One Container: Add the lateral area and the top and bottom areas together.
- Total surface area = [tex]\( 51.8 + 47.4 = 99.3 \)[/tex] square inches.
3. Calculate the Total Surface Area for 8 Containers:
- Multiply the surface area of one container by 8: [tex]\( 99.3 \times 8 = 794.4 \)[/tex] square inches.
Therefore, the minimum amount of plastic wrap needed to completely wrap 8 containers is 794.4 square inches.
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