Posted by Nikki on Wednesday, May 21, 2008 at 8:49pm.
A cylindrical solid has a cylindrical circular hold drilled out of the center. Bascially, it's a circular cylinder with a hollow spot right down the middle. Find the surface area of the resulting solid.
radius of larger circle: 2in
radius of smaller circle (hollow area): 1in
height: 3in
I got this problem wrong on the test, but here's what I did:
I used the formula for the surface area of a cylinder. I found the surface area for the entire cylinder, which was 20pi. Then found the area of the smaller circles, and got 2pi. My resulting answer was 18pi.
Can someone show me where I went wrong? Thanks!

Math  Geometry  bobpursley, Wednesday, May 21, 2008 at 8:58pm
surface area of two end: PI(42)* two ends
surface are of outer : PI*2*3
surface area of inner: PI*1*3
Total area: PI (3+6+2)
check my thinking.

Math  Geometry  Nikki, Wednesday, May 21, 2008 at 9:06pm
Another question, hehe: By "two ends", you mean the radii of the circles?

Math  Geometry  Reiny, Wednesday, May 21, 2008 at 9:14pm
The way I looked at was this :
Surface area of outside cylinder = 2pi(2) = 4pi .... 2pi(r)(h)
Surface area of inside of cylinder = 2pi(1) = 2pi
Surface area of top ("washer" shape) = pi(2^2)  pi(1^2) = 3pi
Now the question becomes whether to include the base in the surface area calculation.
Students in the last few days have been using the definition lateral surface area to exclude the base.
So if we include the base the total surface area would be 4pi + 2pi + 6pi = 12pi
if we exclude it then 9pi

Math  Geometry  bobpursley, Wednesday, May 21, 2008 at 10:28pm
Reiny is right on the ends, 3PI for each. I included the base.

Math  Geometry  tchrwill, Thursday, May 22, 2008 at 11:08am
Find the surface area of the resulting SOLID.
R = 2, r = 1, h = 3
Outer
Outer cylinder = 2R(Pi)h
Outer cylinder = 2(2)Pi(3) = 12Pi
Inner cylinder = 2r(Pi)h
Inner cylinder = 2(1)Pi(3) = 6Pi
Ends = [PiR^2  Pi(1^2)]2
Ends = [Pi(2^2)Pi(1^2)]2 = 6Pi
Total surface area = 24Pi
WHERE DID I GO WRONG, IF I DID??
Lateral surface area of cylinder standing on one end = 2(2)Pi(3) = 12Pi
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