Adrian is painting the outside of a cylinder that he plans to use as a coffee table. The cylinder has a radius of 4 feet and a height of 3 feet Adrian wants to paint all around the outside of the cylinder including the top and bottom faces in order to understand how much paint is needed. He wants to know the surface area of the outside of the cylinder. What is the surface area of the cylinder measured in square feet? Why is the answer 175.8 and NOT 175.9
To calculate the surface area of the outside of the cylinder, we need to calculate the area of the curved part (lateral surface area) and the area of the top and bottom faces.
The lateral surface area of a cylinder is given by the formula: 2πrh, where r is the radius and h is the height.
Lateral surface area = 2π(4)(3) = 24π ≈ 75.4 ft²
The area of each circular face is given by the formula: πr², where r is the radius.
Area of the top and bottom faces = 2π(4)² = 32π ≈ 100.5 ft²
To find the total surface area, we add the lateral surface area and the area of the top and bottom faces:
Total surface area = lateral surface area + area of top and bottom faces
Total surface area = 75.4 + 100.5
Total surface area ≈ 175.9 ft²
In this case, the total surface area is rounded to the nearest tenth, which gives us 175.9 ft². However, since the question asks for the surface area measured in square feet, the answer should be rounded to the nearest whole number. Rounded to the nearest whole number, the surface area of the cylinder is 176 ft².
Therefore, the answer should be 176 ft², not 175.8 or 175.9 ft².