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 331.27 ft.2 331.27 ft. squared 4,182.48 ft.2 4,182.48 ft. squared 27.475 ft.2 27.475 ft. squared 29.045 ft.2
To find the surface area of the can, we first need to find the lateral surface area and then add the area of the top and bottom of the can.
The lateral surface area of a cylinder is calculated using the formula:
Lateral surface area = 2 * π * radius * height
First, convert the radius to inches:
0.5 feet = 0.5 * 12 = 6 inches
Now, calculate the lateral surface area:
Lateral surface area = 2 * 3.14 * 6 * 105
Lateral surface area = 1,979.4 in^2
Next, calculate the area of the top and bottom of the can (two circles):
Area of one circle = π * radius^2
Area of one circle = 3.14 * 6^2
Area of one circle = 113.04 in^2
Total area of top and bottom = 2 * 113.04
Total area of top and bottom = 226.08 in^2
Add all the areas together to find the total surface area:
Total surface area = Lateral surface area + Total area of top and bottom
Total surface area = 1,979.4 + 226.08
Total surface area = 2,205.48 in^2
Finally, convert the total surface area to square feet:
To convert square inches to square feet, divide by 144:
2,205.48 in^2 / 144 = 15.34 ft^2
Therefore, the can's surface area is approximately 15.34 ft^2.