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 of 3.14 for pi.
(1 point)
Responses
1. 252.77 yards
2. 252.77 square yards
3. 329.7 square yards
4. 577.76 square yards
To find the surface area of a cylinder, you need to calculate the sum of the areas of the two bases and the lateral surface.
The area of each base can be found using the formula for the area of a circle: A = πr^2, where π is approximately 3.14 and r is the radius.
So, the area of each base is approximately A = 3.14 * 7^2 = 3.14 * 49 = 153.86 square yards.
The lateral surface area can be found using the formula for the lateral surface area of a cylinder: A = 2πrh, where r is the radius and h is the height.
So, the lateral surface area is approximately A = 2 * 3.14 * 7 * 8 = 351.68 square yards.
Now, we can calculate the surface area by adding the areas.
Surface area = (2 * base area) + lateral surface area
Surface area = (2 * 153.86) + 351.68
Surface area = 307.72 + 351.68
Surface area = 659.4 square yards
Therefore, the correct answer is 4. 659.4 square yards.
thats not an answer
I apologize for the confusion. To clarify, the correct answer is 659.4 square yards, not 577.76 square yards.
To find the surface area of a cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area.
The area of a circle is given by the formula A = πr^2, where π is the approximate value of 3.14 and r is the radius of the circle.
For the bases of the cylinder, we have two circles with the same radius of 7 yards. Therefore, the total area of the bases is 2 * (3.14 * 7^2).
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius of the cylinder's base and h is its height.
The lateral surface area of the cylinder is 2 * (3.14 * 7 * 8).
To find the total surface area, we add the areas of the bases and the lateral surface area: 2 * (3.14 * 7^2) + 2 * (3.14 * 7 * 8).
Simplifying this equation, we get: 2 * (3.14 * 49) + 2 * (3.14 * 7 * 8) = 307.86 + 351.68 = 659.54 square yards.
Therefore, the surface area of the cylinder is approximately 659.54 square yards.
Thus, the correct answer is option 4. 577.76 square yards.