Cones, Cylinders, & Spheres Unit Test
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Question 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)
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To find the surface area of a cylinder, we need to find the sum of the areas of the two circular bases and the lateral surface area.
The area of a circular base is given by the formula A = πr^2, where r is the radius.
In this case, the radius of the cylinder is 4 feet. Therefore, the area of each circular base is A = 3.14 * 4^2 = 3.14 * 16 = 50.24 square feet.
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height.
In this case, the height of the cylinder is 3 feet. Therefore, the lateral surface area is A = 2 * 3.14 * 4 * 3 = 75.36 square feet.
To find the total surface area, we add the areas of the two circular bases and the lateral surface area:
Total Surface Area = 2 * (A of circular base) + (lateral surface area)
Total Surface Area = 2 * 50.24 + 75.36
Total Surface Area = 100.48 + 75.36
Total Surface Area = 175.84
Therefore, the surface area of the cylinder is approximately 175.84 square feet.