A large cylinder-shaped cushion has a height of 1 foot and a diameter of 4 feet. How many square feet of fabric will be need to reupholster the entire cushion? Use 3.14 for pi.(1 point)%0D%0AResponses%0D%0A%0D%0A12.56 square feet%0D%0A12.56 square feet%0D%0A%0D%0A25.12 square feet%0D%0A25.12 square feet%0D%0A%0D%0A125.6 square feet
To find the surface area of the cushion, we need to find the area of the two circular ends and the curved surface area.
The area of the circular ends can be found using the formula for the area of a circle: A = πr^2. Since the diameter is given, we need to divide it by 2 to get the radius.
Radius = Diameter/2 = 4 feet / 2 = 2 feet
Area of each circular end = π(2 feet)^2 = 4π square feet (approximately 12.56 square feet)
The curved surface area can be found using the formula: A = 2πrh, where r is the radius and h is the height.
Curved surface area = 2π(2 feet)(1 foot) = 4π square feet (approximately 12.56 square feet)
Adding the two areas together:
Total surface area = 12.56 square feet + 12.56 square feet = 25.12 square feet
Therefore, we would need approximately 25.12 square feet of fabric to reupholster the entire cushion.