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 are of the outside of the cylinder. What is the surface area of the cylinder, measured in square feet? use 3.14 for pi and round your answer to the nearest tenth.(1 point)
The surface area of the cylinder consists of the curved lateral surface area and the areas of the top and bottom faces.
The curved lateral surface area can be calculated using the formula: A = 2πrh, where r is the radius and h is the height.
A = 2 * 3.14 * 4 * 3
A = 75.36 square feet
The area of each circle (top and bottom faces) can be calculated using the formula: A = πr^2
A = 3.14 * 4^2
A = 50.24 square feet
To find the total surface area, we add the lateral surface area and the areas of the top and bottom faces:
Total surface area = 75.36 + 50.24 + 50.24 = 175.84 square feet
Therefore, the surface area of the cylinder is 175.84 square feet.
wrong
I apologize for the incorrect response. Let's calculate the surface area of the cylinder correctly.
The curved lateral surface area of the cylinder can be calculated using the formula: A = 2πrh, where r is the radius and h is the height.
A = 2 * 3.14 * 4 * 3
A = 75.36 square feet
The area of each circle (top and bottom faces) can be calculated using the formula: A = πr^2
A = 3.14 * 4^2
A = 50.24 square feet
To find the total surface area, we add the lateral surface area and the areas of the top and bottom faces:
Total surface area = 75.36 + 50.24 + 50.24 = 175.84 square feet
Therefore, the surface area of the cylinder is 175.84 square feet.
To calculate the surface area of the outside of the cylinder, we need to find the area of the curved surface plus the areas of the top and bottom faces.
The curved surface area of a cylinder can be calculated using the formula:
CSA = 2 * pi * r * h
where CSA is the curved surface area, pi is a mathematical constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, the radius (r) is 4 feet and the height (h) is 3 feet. So we have:
CSA = 2 * 3.14 * 4 * 3
CSA = 75.36 square feet (rounded to the nearest tenth)
The area of each circular face (top and bottom) can be calculated using the formula:
Area = pi * r^2
where Area is the area of the circular face, pi is the mathematical constant 3.14, and r is the radius of the cylinder.
In this case, the radius (r) is 4 feet. So we have:
Area = 3.14 * 4^2
Area = 50.24 square feet (rounded to the nearest tenth)
To find the total surface area, add the curved surface area to the areas of the top and bottom faces:
Total Surface Area = CSA + 2 * Area
Total Surface Area = 75.36 + 2 * 50.24
Total Surface Area = 75.36 + 100.48
Total Surface Area = 175.84 square feet (rounded to the nearest tenth)
Therefore, the surface area of the outside of the cylinder is approximately 175.8 square feet.