Use the image to answer the question.

Question

A cylinder is labeled with a height of 8 yards and a radius of 7 yards.



Find the surface area of the cylinder. Use the approximation 3.14 for pi.

(1 point)
Responses

577.76 square yards
577.76 square yards

329.7 square yards
329.7 square yards

252.77 square yards
252.77 square yards

252.77 yards

Answer 1

To find the surface area of a cylinder, we need to calculate the area of the two bases and the lateral surface area.

The area of each base can be found using the formula for the area of a circle:

Area of base = π * radius^2

Substituting in the given radius of 7 yards, we have:

Area of base = 3.14 * 7^2 = 3.14 * 49 = 153.86 square yards (approximate)

Since there are two bases, the total area for the bases is:

Total area for bases = 2 * Area of base = 2 * 153.86 = 307.72 square yards (approximate)

The lateral surface area of a cylinder is given by the formula:

Lateral surface area = 2 * π * radius * height

Substituting in the given radius of 7 yards and the given height of 8 yards, we have:

Lateral surface area = 2 * 3.14 * 7 * 8 = 351.68 square yards (approximate)

To find the total surface area, we add the area of the bases to the lateral surface area:

Total surface area = Total area for bases + Lateral surface area = 307.72 + 351.68 = 659.4 square yards (approximate)

Therefore, the surface area of the cylinder is approximately 659.4 square yards.

Answer 2

Wrong

Answer 3

I apologize for the incorrect response. Let's calculate the surface area of the cylinder using the correct method.

The surface area of a cylinder is given by the formula:

Surface area = 2πr(r + h)

Given the radius as 7 yards and height as 8 yards, we can substitute these values into the formula:

Surface area = 2 * 3.14 * 7(7 + 8)

Surface area = 2 * 3.14 * 7 * 15

Surface area = 2 * 3.14 * 105

Surface area = 659.4 square yards (approximate)

Therefore, the correct answer is 659.4 square yards.