Adrián 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 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?
The surface area of the side of the cylinder can be found using the formula for the lateral surface area of a cylinder:
Lateral Surface Area = 2πrh
Where r is the radius and h is the height of the cylinder.
In this case, the radius (r) is 4 feet and the height (h) is 3 feet.
Lateral Surface Area = 2π(4)(3) = 24π square feet.
The surface area of the top and bottom faces of the cylinder can be found using the formula for the area of a circle:
Area = πr^2
Where r is the radius of the circle.
In this case, the radius (r) is 4 feet.
Area = π(4^2) = 16π square feet.
Since there are two faces (top and bottom), the total area of the top and bottom faces is:
2(16π) = 32π square feet.
To find the total surface area of the outside of the cylinder, we need to add the lateral surface area to the total area of the top and bottom faces.
Total Surface Area = Lateral Surface Area + Total Area of Top and Bottom Faces
Total Surface Area = 24π + 32π
Total Surface Area = 56π square feet.
Therefore, the surface area of the outside of the cylinder is 56π square feet.