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.(1 point) cm2
get the exact answer
First, we need to find the surface area of the lateral surface of the cylinder, which can be calculated using the formula:
Surface Area = 2πrh
Where:
r = radius of the cylinder = 0.5 cm / 2 = 0.25 cm
h = height of the cylinder = 19 cm
Surface Area = 2 * 3.14 * 0.25 * 19
Surface Area = 29.9 cm2
Next, we need to find the surface area of the two circular bases of the cylinder:
Surface Area = 2πr2
Surface Area = 2 * 3.14 * 0.25^2
Surface Area = 2 * 3.14 * 0.0625
Surface Area = 0.3925 cm2
Now, add the surface area of the lateral surface and the two circular bases together to get the total surface area of Ming's bundle of pencils:
Total Surface Area = Surface Area of lateral surface + 2 * Surface Area of bases
Total Surface Area = 29.9 + 2 * 0.3925
Total Surface Area = 30.7 cm2
Therefore, the surface area of Ming's bundle of pencils is 30.7 cm2.
that is not the answer
I apologize for the mistake. Let's recalculate the surface area of Ming's bundle of pencils:
Given:
- Diameter = 0.5 cm (so radius = 0.5/2 = 0.25 cm)
- Length = 19 cm
To find the total surface area, we need to calculate the surface area of the lateral surface (cylinder) and the two circular bases.
1. Surface Area of the lateral surface (cylinder):
Surface Area = 2πrh
Surface Area = 2 * 3.14 * 0.25 * 19
Surface Area = 2 * 3.14 * 4.75
Surface Area = 29.86 cm2
2. Surface Area of the two circular bases:
Each base has an area of πr2
Each base = 3.14 * 0.25^2
Each base = 3.14 * 0.0625
Each base = 0.19625 cm2
Both bases = 2 * 0.19625 = 0.3925 cm2
Total Surface Area = Lateral Surface Area + 2 * Base Area
Total Surface Area = 29.86 + 0.3925
Total Surface Area = 30.2525 cm2
Rounded to the nearest tenth, the surface area of Ming's bundle of pencils is 30.3 cm2.
that is not the answer what is the correct exact answer
I apologize for the errors in the previous calculations. Let's correct that and find the exact answer for the surface area of Ming's bundle of pencils.
Given:
- Diameter = 0.5 cm (so radius = 0.5/2 = 0.25 cm)
- Length = 19 cm
We need to find the surface area of the lateral surface (cylinder) and the two circular bases and then add them together.
1. Surface Area of the lateral surface:
Surface Area = 2πrh
Surface Area = 2 * 3.14 * 0.25 * 19
Surface Area = 2 * 3.14 * 4.75
Surface Area = 29.86 cm2
2. Surface Area of the two circular bases:
Each base has an area of πr^2
Each base = 3.14 * 0.25^2
Each base = 3.14 * 0.0625
Each base = 0.19625 cm2
Both bases = 2 * 0.19625 = 0.3925 cm2
Total Surface Area = Lateral Surface Area + 2 * Base Area
Total Surface Area = 29.86 + 0.3925
Total Surface Area = 30.2525 cm2
Therefore, the correct exact answer for the surface area of Ming's bundle of pencils is 30.2525 square centimeters.