Asked by the rose song
ind the surface area of the cylinder. Use the approximation 3.14 for pi. 7yd. 8yd.
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Answered by
GPT 3.5
To find the surface area of a cylinder, you need to find the sum of the areas of the two bases and the lateral surface area.
The base of the cylinder is a circle, so you can find the area of each base by using the formula:
Area of a circle = π * radius^2
In this case, the radius is half the diameter, which is 7yd/2 = 3.5yd.
So, the area of one base is:
Area of base = 3.14 * (3.5yd)^2 = 3.14 * 12.25yd^2 = 38.465yd^2 (approximated)
Since there are two bases, the total area of the bases is 2 times the area of one base.
Total area of bases = 2 * 38.465yd^2 = 76.93yd^2 (approximated)
The lateral surface area of a cylinder is the area of the curved surface, which is found by multiplying the circumference of the base by the height of the cylinder.
Circumference of base = 2 * π * radius = 2 * 3.14 * 3.5yd = 21.98yd (approximated)
Height of the cylinder = 8yd
Lateral surface area = Circumference of base * Height of cylinder = 21.98yd * 8yd = 175.84yd^2 (approximated)
Finally, to find the total surface area, you just need to sum the area of the bases and the lateral surface area:
Total surface area = Total area of bases + Lateral surface area = 76.93yd^2 + 175.84yd^2 = 252.77yd^2 (approximated)
Therefore, the surface area of the cylinder is approximately 252.77 square yards.
The base of the cylinder is a circle, so you can find the area of each base by using the formula:
Area of a circle = π * radius^2
In this case, the radius is half the diameter, which is 7yd/2 = 3.5yd.
So, the area of one base is:
Area of base = 3.14 * (3.5yd)^2 = 3.14 * 12.25yd^2 = 38.465yd^2 (approximated)
Since there are two bases, the total area of the bases is 2 times the area of one base.
Total area of bases = 2 * 38.465yd^2 = 76.93yd^2 (approximated)
The lateral surface area of a cylinder is the area of the curved surface, which is found by multiplying the circumference of the base by the height of the cylinder.
Circumference of base = 2 * π * radius = 2 * 3.14 * 3.5yd = 21.98yd (approximated)
Height of the cylinder = 8yd
Lateral surface area = Circumference of base * Height of cylinder = 21.98yd * 8yd = 175.84yd^2 (approximated)
Finally, to find the total surface area, you just need to sum the area of the bases and the lateral surface area:
Total surface area = Total area of bases + Lateral surface area = 76.93yd^2 + 175.84yd^2 = 252.77yd^2 (approximated)
Therefore, the surface area of the cylinder is approximately 252.77 square yards.
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