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

Question

get the exact answer

Answer 1

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.

Answer 2

that is not the answer

Answer 3

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.

Answer 4

that is not the answer what is the correct exact answer

Answer 5

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.