A cylinder has a height of 15 feet and a radius of 4 feet. Solve for the total surface area of the cylinder. Use 3.14 for 𝝿 and round ot the nearest tenth.
a 56.52 feet^2
b 301.44 feet^2
c 60 feet^2
d 477.3 feet^2
To find the total surface area of a cylinder, you need to calculate the areas of the two bases and the curved surface.
The area of each base (which is a circle) is given by the formula:
Area of circle = π * radius²
Substituting the given values, we find:
Area of each base = 3.14 * 4² = 3.14 * 16 = 50.24 feet²
The curved surface is a rectangle that wraps around the cylinder. Its height is equal to the height of the cylinder (15 feet), and its length is equal to the circumference of the base.
Circumference of circle = 2 * π * radius
Substituting the given values, we find:
Circumference of base = 2 * 3.14 * 4 = 25.12 feet
Therefore, the curved surface area is:
Curved surface area = height * circumference of base = 15 * 25.12 = 376.8 feet²
To find the total surface area, add the areas of the two bases and the curved surface:
Total surface area = 2 * area of each base + curved surface area
Total surface area = 2 * 50.24 + 376.8 = 100.48 + 376.8 = 477.28 feet²
Rounded to the nearest tenth, the total surface area is:
Total surface area ≈ 477.3 feet²
Therefore, the correct answer is option d) 477.3 feet².