# geometry proplem I dont understand **URL:** \ **Category:** Factual Questions\ **Created:** [September 20, 2007, 11:23pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925 "2007-09-20T23:23:31Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 20, 2007, 11:23pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/1 "2007-09-20T23:23:31Z")
Here is the problem, that I do not really understand.: A Company is decreasing by 10 % the amount of tuna sold in cylindrical cans. The cans will have the same height but a smaller diameter to minimize the impact on consumer when they see the smaller can. By what % should the diameter be decreased to accomodate the change? ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 20, 2007, 11:25pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/2 "2007-09-20T23:25:09Z")
I’m not sure what the policy is here on people with homework questions, but you could start by figuring out the formula for the volume of a cylinder in terms of its diameter and height, and going from there. ---
**Author:** ![bstenger](https://avatars.discourse-cdn.com/v4/letter/b/54ee81/32.png) [@bstenger](https://boards.straightdope.com/u/bstenger)\ **Post date:** [September 20, 2007, 11:27pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/3 "2007-09-20T23:27:34Z")
[QUOTE=Indistinguishable] I’m not sure what the policy is here on people with homework questions, but you could start by figuring out the formula for the volume of a cylinder in terms of its diameter and height, and going from there. [/QUOTE] You don’t understand the problem (what’s being asked), or you don’t know how to get the answer? ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [September 20, 2007, 11:31pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/4 "2007-09-20T23:31:26Z")
[QUOTE=bstenger] You don’t understand the problem (what’s being asked), or you don’t know how to get the answer? [/QUOTE] Traditionally, we don’t do homework problems here. I believe **Indistinguishable** was making a suggestion that would put **dauerbach** on the right track to solving the problem. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 20, 2007, 11:33pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/5 "2007-09-20T23:33:06Z")
[QUOTE=KneadToKnow] Traditionally, we don’t do homework problems here. I believe **Indistinguishable** was making a suggestion that would put **dauerbach** on the right track to solving the problem. [/QUOTE] Precisely. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [September 20, 2007, 11:33pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/6 "2007-09-20T23:33:27Z")
I’d suggest they’re better off not retooling and just put more oil in the cans. Anyhoo… Area of the old can lid (I assume the can is cylindrical): π_r_[sup]2[/sup] Area of new, smaller can lid: π(_r-x_)[sup]2[/sup] Solve for _x_ such that the second value is 90% of the first. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 20, 2007, 11:42pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/7 "2007-09-20T23:42:11Z")
I understand what is being asked, but, to my eyes, there does not seem to be enough information given to answer the question. It is a commonly encountered problem, the manufacturer decreases the amount of product in an item. Generally, they just keep the package the same size. I just don’t see where enough information is given to solve the problem. I know that the volume of a cylinder is pi_r^2_h. Maybe I am just having a bad day, but I cant seem to come up with the appropriate equation. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [September 20, 2007, 11:52pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/8 "2007-09-20T23:52:30Z")
[QUOTE=dauerbach] I understand what is being asked, but, to my eyes, there does not seem to be enough information given to answer the question. It is a commonly encountered problem, the manufacturer decreases the amount of product in an item. Generally, they just keep the package the same size. I just don’t see where enough information is given to solve the problem. I know that the volume of a cylinder is pi_r^2_h. Maybe I am just having a bad day, but I cant seem to come up with the appropriate equation. [/QUOTE] Ok, say you have a box with sides x, y, and z. You need a new box with 90% of the volume and two sides are the same, can you figure that one out? xyw needs to be 90% of xyz. where w is the new height. If you can figure that out, how is that similar to a cylinder? ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [September 20, 2007, 11:58pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/9 "2007-09-20T23:58:49Z")
**dauerbach** , keep in mind that decreasing by 10% is the same as multiplying by 0.9. Maybe that will help. ---
**Author:** ![aerodave](https://avatars.discourse-cdn.com/v4/letter/a/f08c70/32.png) [@aerodave](https://boards.straightdope.com/u/aerodave)\ **Post date:** [September 20, 2007, 11:59pm UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/10 "2007-09-20T23:59:01Z")
I suspect you feel there isn’t enough information because you don’t have a known volume in the original can. But since we’re dealing with a percent change, you can definitely do the problem. The problem reduces to asking "How much of a reduction in _r_ results in a 10% reduction in _V_ in the equation _V_ = _πr_[sup]2[/sup]_h_ ? Put another way, if a value of _r_ gives you _V_, what value (in terms of _r_) gives you 0.9_V_ ? ---
**Author:** ![gigi](https://avatars.discourse-cdn.com/v4/letter/g/a587f6/32.png) [@gigi](https://boards.straightdope.com/u/gigi)\ **Post date:** [September 21, 2007, 12:01am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/11 "2007-09-21T00:01:05Z")
The proportion of the new volume to the old volume is .90. pi and h cancel out so Rnew^2/Rold^2 = .90 Manipulate and get a proportion between Rnew and Rold expressed as a percentage. ?? ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [September 21, 2007, 12:01am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/12 "2007-09-21T00:01:26Z")
[QUOTE=dauerbach] I understand what is being asked, but, to my eyes, there does not seem to be enough information given to answer the question. It is a commonly encountered problem, the manufacturer decreases the amount of product in an item. Generally, they just keep the package the same size. I just don’t see where enough information is given to solve the problem. I know that the volume of a cylinder is pi_r^2_h. Maybe I am just having a bad day, but I cant seem to come up with the appropriate equation. [/QUOTE] Ok so the equation for the volume of a cylinder has two variables, r and h. “h” is constant in this scenario, so only r is in the equation. The equation you want to solve is 90%\*old volume=new volume. Plug in the equations for the volumes using r[sub]old[/sub] and r[sub]new[/sub]. Then use algebra to get to a point where you have r[sub]new[/sub]=r[sub]old[/sub]_X, where X will be some coefficient. Then (1-x)100 will get you the percentage you have to reduce r. .9pi_r[sub]old[/sub][sup]2[/sup]_h=pi_r[sub]new[/sub][sup]2[/sup]\*h cancel out pi and h. .9\*r[sub]old[/sub][sup]2[/sup]=r[sub]new[/sub][sup]2[/sup] square root both sides: .95\*r[sub]old[/sub]=r[sub]new[/sub] X is .95, (1-.95)\*100% equals 5%. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 21, 2007, 12:15am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/13 "2007-09-21T00:15:03Z")
Thanks, I was working on this for over an hour. I guess is is just getting my brain into calculate mode. I thank you for your assistance. I often check problems at this site. This is one of the few times my brain went totally offline. It seems so easy now. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 21, 2007, 12:16am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/14 "2007-09-21T00:16:37Z")
If you don’t feel there’s enough information to solve the problem, then think to yourself “What more information do I need in order to solve this?”. Now pretend you had that information. What would you do at this point to solve the problem? You can write all those steps down and end up getting the answer in terms of variables representing the unknown information you feel you need. At this point, you can analyze that answer and see if those variables actually cancel out or end up otherwise irrelevant to the final answer; if they do, then you’ve got your answer without needing to actually find out the value of those variables; hooray! If they don’t, then you’ve done all you can (gotten an expression for the final answer which can be evaluated as soon as unknown but necessary further information is plugged into it). But in this case, it should be the former and not the latter. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 21, 2007, 12:18am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/15 "2007-09-21T00:18:43Z")
Also, I am not so brain dead that I didn’t notice that the radius decreases by 5%, but the question concerns diameter, which decreases by 10%.(2 \* r). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 21, 2007, 12:20am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/16 "2007-09-21T00:20:28Z")
[QUOTE=dauerbach] Also, I am not so brain dead that I didn’t notice that the radius decreases by 5%, but the question concerns diameter, which decreases by 10%.(2 \* r). [/QUOTE] Better rethink that. I’ll put it this way: when we say X decreases by 5%, we normally mean that X moves to a quantity which is 95% of what X used to be. If the radius moves to a quantity which is 95% of what it used to be, then what happens to the diameter? ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [September 21, 2007, 12:21am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/17 "2007-09-21T00:21:48Z")
r[sup]2[/sup] is the only value that changes here, so you know that the new r[sup]2[/sup] has a value of 0.9 times the old r[sup]2[/sup]. The square root of 0.9 is 0.9486832981 In whatever units you measure the diameter in, inches, meters or furlongs, the new smaller can will measure 94.86832981% of the diameter of the old can. ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 21, 2007, 12:22am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/18 "2007-09-21T00:22:54Z")
Alright, I am brain dead. If the radius decreases by 5% then the diameter decreases by 2.5%. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 21, 2007, 12:24am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/19 "2007-09-21T00:24:23Z")
Well, why don’t we try some examples? The radius starts out 100 inches. The diameter, therefore, starts out 200 inches. The radius changes to 95 inches. What does the diameter change to? What percentage change is this? ---
**Author:** ![dauerbach](https://avatars.discourse-cdn.com/v4/letter/d/c2a13f/32.png) [@dauerbach](https://boards.straightdope.com/u/dauerbach)\ **Post date:** [September 21, 2007, 12:25am UTC](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925/20 "2007-09-21T00:25:08Z")
Damn, it seems that my brain is fried tonight. [Next page](https://boards.straightdope.com/t/geometry-proplem-i-dont-understand/419925.md?page=2)