SOLUTION: A tube has the radius of 3cm and a height of 8cm, what is the surface of the tube

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Question 616163: A tube has the radius of 3cm and a height of 8cm, what is the surface of the tube
Answer by dragonwalker(73) About Me  (Show Source):
You can put this solution on YOUR website!
I don't want to confuse, but is it an open ended tube so there is only the body that actually has a surface area or is it a solid cylinder.
Rather than just giving a formula which you can get anywhere I will give you an approach that will show the logic.
To find the surface area of the middle without the two ends think of a paper towel roll. If you cut along and then opened it up you would end up with a rectangle where in this case the length would be 8cm and the width would be the circumference of the circle.
So first find the circumference by using the formula 2 pi r.
r=3 so the circumference is 6 pi = 18.85
So to get the area of the rectangle you multiply length by width as so
18.85 x 8.00 = 150.80 cm^2
If you need to add the surface of both ends then you just need to add the surface area of the two circles.
The formula to find one of the circles is pi r%5E2
so pi x 3%5E2 = 9 pi
= 28.27
we have two circles so the total for both is 28.27 x 2 = 56.54
So add the two circles and the rectangle areas to get the total surface area of a solid tube:
150.80 + 56.54 = 207.34