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.
Surface Area of Cylinders Practice
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4 of 54 of 5 Items
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
11 answers
wrong
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.
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.
wrong
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.
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.
wrong still
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.
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.
wrong...
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.
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.
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.
Let's calculate the surface area of Ming's bundle of unsharpened pencils in the shape of a cylinder step by step:
1. Calculating the lateral surface area:
Lateral Surface Area = 2 * 3.14 * 0.25 * 19
Lateral Surface Area = 3.14 * 0.25 * 38
Lateral Surface Area = 3.14 * 9.5
Lateral Surface Area = 29.83 cm²
2. Calculating the area of the circular bases:
Base Area = 2 * 3.14 * 0.25^2
Base Area = 2 * 3.14 * 0.0625
Base Area = 2 * 0.19625
Base Area = 0.3925 cm²
3. Total Surface Area:
Total Surface Area = Lateral Surface Area + 2 * Base Area
Total Surface Area = 29.83 + 2 * 0.3925
Total Surface Area = 29.83 + 0.785
Total Surface Area ≈ 30.61 cm²
Therefore, the surface area of Ming's bundle of pencils is approximately 30.61 cm² when rounded to the nearest tenth. Thank you for your patience, and I hope this calculation is correct.
1. Calculating the lateral surface area:
Lateral Surface Area = 2 * 3.14 * 0.25 * 19
Lateral Surface Area = 3.14 * 0.25 * 38
Lateral Surface Area = 3.14 * 9.5
Lateral Surface Area = 29.83 cm²
2. Calculating the area of the circular bases:
Base Area = 2 * 3.14 * 0.25^2
Base Area = 2 * 3.14 * 0.0625
Base Area = 2 * 0.19625
Base Area = 0.3925 cm²
3. Total Surface Area:
Total Surface Area = Lateral Surface Area + 2 * Base Area
Total Surface Area = 29.83 + 2 * 0.3925
Total Surface Area = 29.83 + 0.785
Total Surface Area ≈ 30.61 cm²
Therefore, the surface area of Ming's bundle of pencils is approximately 30.61 cm² when rounded to the nearest tenth. Thank you for your patience, and I hope this calculation is correct.
1 answer