Use the image to answer the question.
A cylinder is labeled with a height of 3 yards and a radius of 2 yards.
Find the surface area of the cylinder. Use the approximation of 3.14 for pi.
(1 point)
Responses
62.8
62.8
75.36
75.36
25.12
25.12
32.97
To find the surface area of a cylinder, we first need to find the lateral area and the area of the two bases.
The lateral area of a cylinder can be calculated by multiplying the height by the circumference of the base. The circumference of a circle can be found using the formula 2 * pi * radius.
Lateral area = height * circumference of base
Lateral area = 3 yards * (2 * 3.14 * 2 yards)
Lateral area = 3 yards * (12.56 yards)
Lateral area = 37.68 square yards
The area of each base can be found by multiplying the area of a circle (pi * radius^2) by 2.
Area of each base = pi * radius^2 * 2
Area of each base = 3.14 * (2 yards)^2 * 2
Area of each base = 3.14 * 4 yards^2 * 2
Area of each base = 3.14 * 8 square yards
Area of each base = 25.12 square yards
To find the total surface area, we add the lateral area and the area of the two bases.
Total surface area = 2 * area of each base + lateral area
Total surface area = 2 * 25.12 square yards + 37.68 square yards
Total surface area = 50.24 square yards + 37.68 square yards
Total surface area = 87.92 square yards
Therefore, the surface area of the cylinder is approximately 87.92 square yards.