Surface Area of Cylinders Practice
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Question
Use the image to answer the question.
An illustration shows a cylinder with diameter, 10 feet, and perpendicular height, 8.5 feet. The cylinder is placed horizontally and the edges that are not visible are represented by a dashed line.
Solve the surface area of the cylinder. Give both exact and approximate answers. Round the approximate answer to the nearest hundredth. Use π=3.14 .
(1 point)
Exact answer:
π m2
Approximate answer:
m2
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To find the surface area of a cylinder, you need to find the area of the two circular bases and the lateral surface area.
1. The area of one circular base is πr^2, where r is the radius. Since the diameter is 10 feet, the radius is half of that, which is 5 feet. So the area of one base is π(5)^2 = 25π square feet.
2. Since there are two bases, the total area of both bases is 2(25π) = 50π square feet.
3. The lateral surface area can be calculated by finding the circumference of the base and multiplying it by the height of the cylinder.
- The circumference of the base is 2πr, which is 2π(5) = 10π feet.
- The height of the cylinder is 8.5 feet.
So the lateral surface area is 10π * 8.5 = 85π square feet.
4. The total surface area is the sum of the two base areas and the lateral surface area:
50π + 85π = 135π square feet.
Therefore, the exact answer is 135π square feet, and the approximate answer is 135π ≈ 424.50 square feet rounded to the nearest hundredth.