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 t
he outside of the cylinder?
To find the surface area of the outside of the cylinder, we need to calculate the area of the two circular bases and the lateral surface area.
The area of one circular base can be found using the formula for the area of a circle: A = πr^2, where r is the radius of the circle. In this case, the radius is 4 feet, so the area of one circular base is A = π(4)^2 = 16π square feet.
Since there are two circular bases, the total area of the two circular bases is 2(16π) = 32π square feet.
The lateral surface area of a cylinder can be found using the formula: A = 2πrh, where r is the radius and h is the height of the cylinder. In this case, r = 4 feet and h = 3 feet, so the lateral surface area is A = 2π(4)(3) = 24π square feet.
Therefore, the total surface area of the outside of the cylinder is the sum of the areas of the two circular bases and the lateral surface area: 32π + 24π = 56π square feet.
Thus, Adrian will need 56π square feet of paint to cover the outside of the cylinder.