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A cylinder is labeled with a height of 8 yards and a radius of 7 yards.
Find the surface area of the cylinder. Use the approximation 3.14 for pi.
(1 point)
Responses
329.7 square yards
329.7 square yards
577.76 square yards
577.76 square yards
252.77 square yards
252.77 square yards
252.77 yards
252.77 yards
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To find the surface area of a cylinder, we need to calculate the sum of the areas of the two bases and the lateral surface area.
The area of each base can be found using the formula for the area of a circle: A = πr², where r is the radius of the base. In this case, the radius is 7 yards, so the area of each base is A = 3.14 × (7)² = 153.86 square yards.
The lateral surface area can be found using the formula A = 2πrh, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 7 yards and the height is 8 yards, so the lateral surface area is A = 2 × 3.14 × 7 × 8 = 351.68 square yards.
Finally, the total surface area of the cylinder is the sum of the two base areas and the lateral surface area: 153.86 + 153.86 + 351.68 = 659.4 square yards.
Since the answer choices are not provided in the exact form, we need to round the answer to the nearest tenth. The final answer is approximately 659.4 square yards.
Therefore, the correct answer is not provided among the given options.
there is an answer, try again.
Apologies for the confusion. Let's re-calculate the surface area of the cylinder.
The area of each base is A = πr² = 3.14 * (7)² = 153.86 square yards.
The lateral surface area is A = 2πrh = 2 * 3.14 * 7 * 8 = 351.68 square yards.
The total surface area of the cylinder is the sum of the two base areas and the lateral surface area: 153.86 + 153.86 + 351.68 = 659.40 square yards.
Therefore, the correct answer is 659.4 square yards, which is not provided among the given options.
are you sure? because thats incorrect
I apologize for the mistake. Let's double-check the calculations.
The area of each base is A = πr² = 3.14 * (7)² = 153.86 square yards.
The lateral surface area is A = 2πrh = 2 * 3.14 * 7 * 8 = 351.68 square yards.
The total surface area of the cylinder is the sum of the two base areas and the lateral surface area: 153.86 + 153.86 + 351.68 = 659.40 square yards.
Since the provided options are not correct, I must have made another error in the calculations. I apologize for the confusion and any inconvenience caused.
can you restart to try solving this error?
Apologies for the confusion. Let's restart the calculation for the surface area of the cylinder.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πrh + 2πr²
Given:
Height (h) = 8 yards
Radius (r) = 7 yards
Pi (π) = 3.14 (approximation)
First, let's calculate the area of the two bases (2πr²).
Area of the base = 2πr² = 2 * 3.14 * 7² = 2 * 3.14 * 49 = 307.72 square yards (approximately)
Next, let's calculate the lateral surface area (2πrh).
Lateral surface area = 2πrh = 2 * 3.14 * 7 * 8 = 351.68 square yards (approximately)
Finally, we add the area of the two bases and the lateral surface area to get the total surface area.
Total Surface Area = 307.72 + 351.68 = 659.4 square yards (approximately)
Therefore, the correct answer is 659.4 square yards.