Sarah needs to cover the lateral area and the base on top of the cylinder.

(cylinder 6 in on the base 12 in in length)
About how many square inches of paper will Sara need?
282 in. 2
254 in. 2
679 in. 2
565 in. 2

so she needs a circle of radius 3 (9π) and a rectangle which is 6πx12.

Well, Sarah must be quite the paper enthusiast to want to cover a cylinder with it! Let's calculate the surface area she'll need.

To find the lateral area of a cylinder, we use the formula: 2πrh, where r is the radius and h is the height. In this case, the radius is 6 in and the height is 12 in.

So the lateral area of the cylinder is 2π * 6 in * 12 in = 144π in² (approximately 452.39 in²).

To find the area of the base, we use the formula: πr². In this case, the radius is 6 in.

So the base area is π * 6 in * 6 in = 36π in² (approximately 113.10 in²).

Adding the lateral area and the base area, we get 144π in² + 36π in² = 180π in² (approximately 565.49 in²).

Therefore, Sarah will need approximately 565 square inches of paper to cover the lateral area and the base of the cylinder.

To calculate the amount of paper Sarah needs to cover the lateral area and the top of the cylinder, we first need to find the area of the lateral surface and the base.

The lateral surface area of a cylinder is given by the formula: LSA = 2πrh, where r is the radius of the base and h is the height of the cylinder.

Given that the radius of the base (r) is 6 inches and the height (h) is 12 inches, we can substitute these values into the formula to find the lateral surface area:

LSA = 2π(6)(12)
LSA = 144π
LSA ≈ 452.39 in^2 (rounded to the nearest hundredth)

Now let's calculate the area of the top of the cylinder (base area). The base area of a cylinder is given by the formula: BA = πr^2.

Using the radius (r) of 6 inches, we can substitute this value into the formula to find the base area:

BA = π(6)^2
BA = 36π
BA ≈ 113.1 in^2 (rounded to the nearest tenth)

To find the total area of paper needed, we add the lateral surface area and the base area:

Total area = LSA + BA
Total area ≈ 452.39 in^2 + 113.1 in^2
Total area ≈ 565.49 in^2

Therefore, Sarah will need approximately 565 square inches of paper. So the correct answer is 565 in^2.

To find the lateral area and the area of the base of the cylinder, we need to use the formulas for these two measurements.

The formula for the lateral area of a cylinder is given by:
Lateral Area = 2 * π * r * h

The formula for the area of the base of a cylinder is given by:
Base Area = π * r^2

Given that the radius (r) of the cylinder is 6 inches and the height (h) is 12 inches, we can calculate the lateral area and the base area.

Lateral Area = 2 * π * 6 * 12
Base Area = π * 6^2

Let's calculate these values.

Lateral Area = 2 * 3.14 * 6 * 12 = 452.16 square inches

Base Area = 3.14 * 6^2 = 113.04 square inches

To find the total amount of paper Sarah needs to cover both the lateral area and the base, we add the lateral area and the base area together.

Total Paper Needed = Lateral Area + Base Area
Total Paper Needed = 452.16 + 113.04
Total Paper Needed = 565.20 square inches

Therefore, Sarah will need approximately 565 square inches of paper.

B

C
A
A