Use the image to answer the question.
A cylinder is labeled with a height of 8 yards and a diameter of 7 yards.
Find the surface area of the cylinder. Use the approximation 3.14 for pi.
(1 point)
Responses
329.7 square yards
329.7 square yards
577.76 square yards
577.76 square yards
252.77 yards
252.77 yards
252.77 square yards
To find the surface area of the cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area.
The area of a base (a circle) is given by the formula A = πr^2, where r is the radius of the circle. The diameter of the cylinder is 7 yards, so the radius is half of that, which is 7/2 = 3.5 yards.
The area of one base is therefore A = 3.14 * (3.5)^2 = 38.465 square yards.
Since the cylinder has two bases, the total area of the bases is 2 * 38.465 = 76.93 square yards.
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height of the cylinder.
The lateral surface area is therefore A = 2 * 3.14 * 3.5 * 8 = 175.84 square yards.
Now, we can calculate the total surface area by adding the area of the bases and the lateral surface area:
Total Surface Area = Base Area + Lateral Surface Area
= 76.93 + 175.84
= 252.77 square yards
So, the surface area of the cylinder is approximately 252.77 square yards.