Use the image to answer the 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
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.
Wrong
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.
To find the surface area of a cylinder, you need to calculate the sum of the areas of its two circular bases and its curved surface. Here's how you can find the surface area using the given dimensions:
1. Find the area of each circular base:
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
In this case, the radius of the cylinder is 7 yards, so the area of each circular base is (3.14)(7)^2 = 153.86 square yards.
2. Find the area of the curved surface:
The formula to find the area of the curved surface of a cylinder is A = 2πrh, where A is the area, r is the radius, and h is the height.
In this case, the height of the cylinder is 8 yards, so the area of the curved surface is (2)(3.14)(7)(8) = 351.68 square yards.
3. Calculate the total surface area:
The total surface area is the sum of the areas of the two circular bases and the curved surface.
Total surface area = 2(area of base) + area of curved surface = 2(153.86) + 351.68 = 307.72 + 351.68 = 659.40 square yards.
So, the correct option is not provided among the responses given. The correct surface area of the cylinder is approximately 659.40 square yards.