Question 101547: a metal pipe is 77 cm. long the inner diameter of a cross section is 4 cm. the outer diameter being 4.8cm. find its
1) inner curved surface area
2) outer curved surface area
3) total surface area
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! The metal pipe is 77 cm long, inner diameter of 4 cm, and outer diameter of 4.8 cm. We can find the inner and outer diamter surface area by finding the outer and inner perimeter and multiplying by the length. The perimeter of a circle is pi x D. The inner perimeter is then 4 pi or 12.57 cm. The outer perimeter is 4.8 pi or 15.08 cm.
1. The inner curved surface area is then the inner perimeter(12.57 cm) multiplied by the length(77 cm) or 967.6 square centimeters.
2. The outer curved surface area is then the outer perimeter(15.08 cm) multiplied by the length(77 cm) or 1161.1 square centimeters.
The total surface area is a little more tricky. There is a small section at the top and bottom of the pipe that is made up of the area between the inner circle and the outer circle that adds to the total surface area. The area of that section is the difference in area between the outer diameter circle and the inner diameter circle.
A = pi/4 x (Do^2 - Di^2) = pi/4 x (4.8^2 - 4.0^2) = 5.5 square centimeters
3. The total surface area is the sum of the inner surface area, the outer surface area, the top surface area, and the bottom surace area or 967.6 + 1161.1 + 5.5 + 5.5. The total surface area is 2139.7 square centimeters. As you can see the top and bottom have a very slight contribution (11 sq. cm) to the total area.
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