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)
To find the surface area of the cushion, we need to find the area of the top and bottom circles, as well as the area of the curved side.
The area of a circle is given by A = πr^2, where r is the radius.
Given that the diameter is 4 feet, we can find the radius by dividing the diameter by 2:
r = 4 feet / 2 = 2 feet
The area of the top and bottom circles is therefore: A_circle = π(2)^2 = 4π square feet.
The cylindrical side can be thought of as a rectangle with one side equal to the height (1 foot) and the other side equal to the circumference of the circle base (2πr).
The circumference of a circle is given by C = 2πr, so the circumference of the base is: C_base = 2π(2) = 4π feet.
The area of the curved side is therefore: A_side = 1 foot * 4π feet = 4π square feet.
To find the total area, we add the areas of the top, bottom, and side:
A_total = A_circle + A_side + A_side = 4π + 4π + 4π = 12π square feet.
Using the approximation 3.14 for π, the total area is approximately:
A_total ≈ 12 * 3.14 ≈ 37.68 square feet.
Therefore, we will need approximately 37.68 square feet of fabric to reupholster the entire cushion.