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.
To find the surface area of the cushion, we need to calculate the area of the circular top and bottom, as well as the area of the curved side.
The area of the circular top and bottom is equal to the area of one circle. The formula to find the area of a circle is A = πr², where r is the radius.
Given that the diameter of the cushion is 4 feet, the radius is half of the diameter, which is 4/2 = 2 feet.
Plugging this value into the formula, we have A = 3.14 * (2)² = 3.14 * 4 = 12.56 square feet.
Since there are two circular ends, the total area for the top and bottom is 2 * 12.56 = 25.12 square feet.
The curved side of the cushion can be thought of as a rectangle. The height of the cushion is 1 foot, and the circumference can be calculated using the formula C = πd, where d is the diameter.
Plugging in the values, we have C = 3.14 * 4 = 12.56 feet.
Since the height of the cushion is 1 foot, the length of the rectangle is equal to the circumference, which is 12.56 feet.
Therefore, the area of the curved side is 12.56 * 1 = 12.56 square feet.
To find the total area for the entire cushion, we add the area of the top and bottom (25.12 square feet) to the area of the curved side (12.56 square feet).
Thus, the total area of fabric needed to reupholster the cushion is 25.12 + 12.56 = 37.68 square feet.