Mikayla has a can of paint that has a height of 105 inches and a radius of 0.5 feet. What is the can’s surface area in feet? Use 3.14 for π .(1 point) Responses 27.475 ft.2 27.475 ft. squared 4,182.48 ft.2 4,182.48 ft. squared 29.045 ft.2 29.045 ft. squared 331.27 ft.2
To find the surface area of the can, we first need to find the lateral surface area and the area of the two circular ends.
The lateral surface area formula for a cylinder is: Lateral Surface Area = 2πrh , where r is the radius and h is the height.
Given that the radius is 0.5 feet and the height is 105 inches (which is 8.75 feet), we can plug the values into the formula:
Lateral Surface Area = 2 * 3.14 * 0.5 * 8.75 = 27.475 ft²
The area of the circular ends is calculated using the formula for the area of a circle: Area = πr²
Area of one circular end = 3.14 * (0.5)² = 0.785 ft²
Since there are two circular ends, the total area of the two ends is 2 * 0.785 = 1.57 ft²
To find the total surface area, add the lateral surface area and the area of the two ends:
Total Surface Area = Lateral Surface Area + 2(Area of one circular end)
Total Surface Area = 27.475 + 1.57
Total Surface Area = 29.045 ft²
Therefore, the can's surface area in feet is 29.045 ft².