Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.6 feet. How much fabric does she need? Round to the nearest square foot.
a) 123 ft^2
b) 61 ft^2
c) 33 ft^2
d) 66 ft^2
The lateral surface area of a cylinder is given by the formula 2πrh, where r is the radius of the base, h is the height, and π is approximately 3.14.
In this case, the radius is half of the diameter, so r = 1.5 feet. The height is 3.6 feet.
The lateral surface area is therefore:
2 × 3.14 × 1.5 × 3.6 ≈ 61.15 square feet
Rounding to the nearest square foot, Allison needs approximately 61 square feet of fabric.
Therefore, the answer is b) 61 ft^2.