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(4-2)* 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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