Question
Find the surface area of the cylinder below. Use the approximation 3.14 for pi. The height is 15 and the diameter
628 centimeters
533.8 square centimeters
1,099 square centimeters
628 square centimeters
628 centimeters
533.8 square centimeters
1,099 square centimeters
628 square centimeters
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Answered by
GPT 3.5
To find the surface area of the cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area.
The base of the cylinder is a circle, and the formula for the area of a circle is A = π * r^2, where r is the radius of the circle. In this case, the diameter is given as 628 centimeters, so the radius is half of that, which is 314 centimeters.
The area of each base is A_base = 3.14 * (314)^2 = 3.14 * 98,596 = 309,133.44 square centimeters.
The lateral surface area of the cylinder is the area of the rectangle formed by rolling the curved surface of the cylinder. The height of the cylinder is given as 15 centimeters, and the circumference of the base (which is also the length of the rectangle) is given as 628 centimeters. So, the formula for the lateral surface area is A_lateral = height * circumference = 15 * 628 = 9,420 square centimeters.
The total surface area of the cylinder is then the sum of the two base areas and the lateral surface area: A_total = 2 * A_base + A_lateral = 2 * 309,133.44 + 9,420 = 627,686.88 square centimeters.
Since we were asked to use the approximation 3.14 for pi, we should round the answer to the nearest whole number, which gives us 628 square centimeters. So, the correct answer is 628 square centimeters.
The base of the cylinder is a circle, and the formula for the area of a circle is A = π * r^2, where r is the radius of the circle. In this case, the diameter is given as 628 centimeters, so the radius is half of that, which is 314 centimeters.
The area of each base is A_base = 3.14 * (314)^2 = 3.14 * 98,596 = 309,133.44 square centimeters.
The lateral surface area of the cylinder is the area of the rectangle formed by rolling the curved surface of the cylinder. The height of the cylinder is given as 15 centimeters, and the circumference of the base (which is also the length of the rectangle) is given as 628 centimeters. So, the formula for the lateral surface area is A_lateral = height * circumference = 15 * 628 = 9,420 square centimeters.
The total surface area of the cylinder is then the sum of the two base areas and the lateral surface area: A_total = 2 * A_base + A_lateral = 2 * 309,133.44 + 9,420 = 627,686.88 square centimeters.
Since we were asked to use the approximation 3.14 for pi, we should round the answer to the nearest whole number, which gives us 628 square centimeters. So, the correct answer is 628 square centimeters.
Answered by
GPT 3.5
Apologies for the mistake in my previous response. Let's correct the calculations.
The diameter of the cylinder is given as 628 centimeters, which means the radius is half of that, or 314 centimeters.
The area of each base can be calculated using the formula A = π * r^2:
A_base = 3.14 * (314)^2 = 3.14 * 98,596 = 309,133.44 square centimeters.
The lateral surface area of the cylinder is the product of the height and the circumference of the base:
circumference = π * diameter = 3.14 * 628 = 1,972.72 centimeters.
A_lateral = height * circumference = 15 * 1,972.72 = 29,590.8 square centimeters.
The total surface area is the sum of the two bases and the lateral surface area:
A_total = 2 * A_base + A_lateral = 2*309,133.44 + 29,590.8 = 647,857.68 square centimeters.
Since the question asks for the surface area to be rounded, we round the answer to the nearest whole number. Therefore, the correct surface area of the cylinder is 648 square centimeters.
I apologize for the confusion in my previous response. The correct answer is 648 square centimeters.
The diameter of the cylinder is given as 628 centimeters, which means the radius is half of that, or 314 centimeters.
The area of each base can be calculated using the formula A = π * r^2:
A_base = 3.14 * (314)^2 = 3.14 * 98,596 = 309,133.44 square centimeters.
The lateral surface area of the cylinder is the product of the height and the circumference of the base:
circumference = π * diameter = 3.14 * 628 = 1,972.72 centimeters.
A_lateral = height * circumference = 15 * 1,972.72 = 29,590.8 square centimeters.
The total surface area is the sum of the two bases and the lateral surface area:
A_total = 2 * A_base + A_lateral = 2*309,133.44 + 29,590.8 = 647,857.68 square centimeters.
Since the question asks for the surface area to be rounded, we round the answer to the nearest whole number. Therefore, the correct surface area of the cylinder is 648 square centimeters.
I apologize for the confusion in my previous response. The correct answer is 648 square centimeters.
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