Surface Area of Cylinders Practice
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Question
Ming has 12 unsharpened pencils bundled in the shape of a cylinder. If the diameter is 0.5 cm and the length is 19 cm, what is the surface area of Ming’s bundle of pencils? Use 3.14 for π and round to the nearest tenth
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I apologize for the errors in the previous calculations. Let's correct it once more:
Given:
Diameter of the cylinder = 0.5 cm
Radius (r) = 0.5 cm / 2 = 0.25 cm
Height (h) = 19 cm
Step 1: Calculate the lateral surface area of one pencil
Lateral Surface Area (A) = 2πrh
A = 2 * 3.14 * 0.25 cm * 19 cm
A = 3.14 * 0.5 cm * 19 cm
A = 29.86 cm²
Step 2: Calculate the total lateral surface area of all 12 pencils
Total Lateral Surface Area = 12 pencils * 29.86 cm²
Total Lateral Surface Area = 358.32 cm²
Therefore, the correct surface area of Ming's bundle of pencils is approximately 358.32 cm². Thank you for your patience.
To find the surface area of the bundle of unsharpened pencils in the shape of a cylinder, we need to calculate the lateral surface area (the area around the side of the cylinder) and the two circular bases' areas.
1. **Calculating the lateral surface area:**
The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height (which is the same as the length of the cylinder).
Given that the diameter is 0.5 cm, the radius (r) is half of the diameter, so r = 0.25 cm. The height (h) is 19 cm.
Substituting these values into the formula:
Lateral Surface Area = 2 * 3.14 * 0.25 * 19
2. **Calculating the area of the circular bases:**
The formula for the area of a circle is πr^2, where r is the radius.
Substituting the radius into the formula:
Base Area = 2 * π * 0.25^2
3. **Total Surface Area:**
To find the total surface area, we sum the lateral surface area and the area of the two circular bases.
Total Surface Area = Lateral Surface Area + 2 * Base Area
Finally, plug in the calculated values to find the total surface area of Ming's bundle of pencils. Remember to round to the nearest tenth as requested.
Step 1: Calculate the radius of the cylinder
Since the diameter is 0.5 cm, the radius is half of the diameter:
radius = 0.5 cm / 2 = 0.25 cm
Step 2: Calculate the surface area of one pencil
The surface area of a cylinder can be calculated using the formula:
Surface area = 2πr(h + r), where r is the radius and h is the height of the cylinder.
Plugging in the values:
Surface area = 2 * 3.14 * 0.25 cm * (19 cm + 0.25 cm)
Surface area = 2 * 3.14 * 0.25 cm * 19.25 cm
Surface area = 3.14 * 0.5 cm * 19.25 cm
Surface area = 3.14 * 9.625 cm
Surface area ≈ 30.2 cm²
Step 3: Calculate the total surface area of all 12 pencils
Since there are 12 pencils, the total surface area would be:
Total surface area = 12 * 30.2 cm²
Total surface area = 362.4 cm²
Therefore, the surface area of Ming's bundle of pencils is approximately 362.4 cm².
I apologize for the mistake. Let's correct the calculation.
Step 1: Calculate the radius of the cylinder
Since the diameter is 0.5 cm, the radius is half of the diameter:
radius = 0.5 cm / 2 = 0.25 cm
Step 2: Calculate the surface area of one pencil
The surface area of a cylinder can be calculated using the formula:
Surface area = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.
Plugging in the values:
Surface area = 2 * 3.14 * (0.25 cm)² + 2 * 3.14 * 0.25 cm * 19 cm
Surface area = 2 * 3.14 * 0.0625 cm² + 2 * 3.14 * 0.25 cm * 19 cm
Surface area = 2 * 0.19625 cm² + 2 * 3.14 * 0.25 cm * 19 cm
Surface area = 0.3925 cm² + 2 * 3.14 * 0.25 cm * 19 cm
Surface area = 0.3925 cm² + 2 * 3.14 * 4.75 cm
Surface area = 0.3925 cm² + 29.83 cm
Surface area ≈ 30.22 cm²
Step 3: Calculate the total surface area of all 12 pencils
Since there are 12 pencils, the total surface area would be:
Total surface area = 12 * 30.22 cm²
Total surface area = 362.64 cm²
Therefore, the correct surface area of Ming's bundle of pencils is approximately 362.64 cm². Thank you for pointing out the error, and I appreciate your understanding.
I apologize for the mistake. Let's correct the calculation:
Step 1: Calculate the radius of the cylinder
Since the diameter is 0.5 cm, the radius is half of the diameter:
radius = 0.5 cm / 2 = 0.25 cm
Step 2: Calculate the surface area of one pencil
Surface area = 2πrh + 2πr², where r is the radius and h is the height of the cylinder.
Plugging in the values:
Surface area of one pencil = 2 * 3.14 * 0.25 cm * 19 cm + 2 * 3.14 * (0.25 cm)²
Surface area of one pencil = 2 * 3.14 * 0.25 cm * 19 cm + 2 * 3.14 * 0.0625 cm²
Surface area of one pencil = 3.14 * 0.5 cm * 19 cm + 3.14 * 0.125 cm²
Surface area of one pencil = 3.14 * 9.5 cm + 0.3925 cm²
Surface area of one pencil ≈ 29.93 cm²
Step 3: Calculate the total surface area of all 12 pencils
Total surface area = 12 pencils * 29.93 cm²
Total surface area = 359.16 cm²
Therefore, the surface area of Ming's bundle of pencils is approximately 359.16 cm². Thank you for your patience.
Apologies for the previous errors. Let's correct the calculation:
Step 1: Calculate the radius of the cylinder
Given diameter = 0.5 cm
Radius (r) = diameter / 2 = 0.5 cm / 2 = 0.25 cm
Step 2: Calculate the surface area of one pencil
Surface area of one pencil = 2πr(r+h)
Surface area = 2 * 3.14 * 0.25(0.25 + 19)
Surface area = 2 * 3.14 * 0.25 * 19.25
Surface area = 3.14 * 0.25 * 19.25
Surface area = 3.14 * 4.8125
Surface area ≈ 15.13 cm²
Step 3: Calculate the total surface area of all 12 pencils
Total surface area = 12 pencils * 15.13 cm²
Total surface area = 181.56 cm²
Therefore, the correct surface area of Ming's bundle of pencils is approximately 181.56 cm². Thank you for your patience.