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| Acmlm's Board - I2 Archive - Brain Teasers - Strange Math Riddles |
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NSNick Laidback Admin Level: 85  Posts: 508/3875 EXP: 5895841 For next: 2699 Since: 03-15-04 From: North Side School: OSU Since last post: 9 hours Last activity: 1 hour |
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| This time I'll do it on paper instead of in my head. [{[7 - (2/7)*7 + 3 - (2/7)*7 - 3]*4}/2]*(4/3) {[(7 - 2 + 3 - 2 - 3)*4]/2}*(4/3) [(3*4)/2]*(4/3) (12/2)*(4/3) 6*(4/3) 8 Eight inches. |
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JJ64 Boo Level: 45 Posts: 492/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| Yay, finally! NSNick gets the point. Scores 1st. wolfman2000-4 points 2nd. NSNick-1 point 2nd. Heian-794-1 point 2nd. Emptyeye-1 point 4th. Kirby all the way-0 points 4th. Teddylot-0 points Question 8 (1 point)- There is a regular hexagon with a side length 6. Find the area and perimeter. |
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NSNick Laidback Admin Level: 85 Posts: 513/3875 EXP: 5895841 For next: 2699 Since: 03-15-04 From: North Side School: OSU Since last post: 9 hours Last activity: 1 hour |
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| The perimeter is 36, obviously. The area is a little more tricky. I found it to be about 93.53 | |||
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JJ64 Boo Level: 45 Posts: 505/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| And another point for NSNick... Scores 1st. wolfman2000-4 points 2nd. NSNick-2 points 3rd. Heian-794-1 point 3rd. Emptyeye-1 point 4th. Kirby all the way-0 points 4th. Teddylot-0 points Question 9 (1 point)- There is a regular decagon with side length 4. Find the measure of each interior angle, each exterior angle, and find out the total sum of the interior and exterior angles combined. (edited by JJ64 on 06-22-04 09:20 AM) |
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wolfman2000 Red Paratroopa Level: 21  Posts: 131/161 EXP: 49927 For next: 16 Since: 03-15-04 Since last post: 471 days Last activity: 339 days |
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| Let's take this a step at a time. The sum of the interior angles for an n sided figure is (n-2) * 180. Therefore, the sum of all of the interior angles for a decagon (a 10 sided figure) is 8 * 180 = 1440. Since there are 10 angles, each interior angle is 1440 / 10 = 144. Now, the part I always forget...how exterior angles are done. If my thinking is correct, it's 180 - interior angle, or in this case, 180 - 144 = 36. That means that all interiors + all exteriors = (36 * 10) + (10 * 144) = 1800. Whew...what a mouthful. |
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Heian-794 Red Super Koopa Level: 44 Posts: 118/896 EXP: 611014 For next: 271 Since: 06-01-04 From: Kyoto, Japan Since last post: 21 days Last activity: 10 days |
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| Wolfman, you're too quick! The rest of us didn't even have a single hour to look at that and solve it! | |||
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JJ64 Boo Level: 45 Posts: 507/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| And wolfman2000 easily gets another point. Another way to find exterior angles is to take 360 divided by the number of sides. Scores 1st. wolfman2000-5 points 2nd. NSNick-2 points 3rd. Heian-794-1 point 3rd. Emptyeye-1 point 4th. Kirby all the way-0 points 4th. Teddylot-0 points I'll continue with Geometry, for fun. Question 10 (1 point)- There is a sphere with a radius 4 in. Find the surface area and volume. Note: Label answers. |
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Grey the Stampede Don't mess with powers you don't understand. And yes. That means donuts. Level: 82  Posts: 22/3770 EXP: 5192909 For next: 16318 Since: 06-17-04 From: Kingston, RI, USA, Earth Since last post: 2 hours Last activity: 1 hour |
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| Easy. Volume's 4/3 (pi)*R^3. That'd be 268.08 cubic inches. Surface area is 4(pi)R^2, which ends up being about 201.06 square inches. Integration is useful. The problem is that I think I'm off in my formulas because I forget whether surface area is the antiderivative of circumference or not cause the formula comes out looking like the area formula. However each polygon generally has a coefficient for 2-dimensional space (for a square it's 1, for a triangle 1/2, for a sphere I think it's 4....), I just can't remember if that one's right for sphere. Also, surface area is a form of 2D area, just stretched over a sphere........... (continues babbling) But yeah, that's my answer. (edited by Grey on 06-22-04 08:23 PM) |
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KATW King Yoshi "If you stare at something long enough, it can be funny." Level: 86  Posts: 960/3959 EXP: 6087979 For next: 54128 Since: 03-15-04 Since last post: 7 hours Last activity: 5 hours |
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| Just as a correction for your math.. Area is 267.95in^3 SA is 200.96in^2 Calculators are helpful  |
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Grey the Stampede Don't mess with powers you don't understand. And yes. That means donuts. Level: 82 Posts: 23/3770 EXP: 5192909 For next: 16318 Since: 06-17-04 From: Kingston, RI, USA, Earth Since last post: 2 hours Last activity: 1 hour |
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Originally posted by Kirby all the way Your reasoning is based off of pi being just 3.14, not 3.1415926535897932......... (that's as far as I can remember it). It's much more precise to use a calculator that has a pi key. |
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JJ64 Boo Level: 45 Posts: 511/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| Hmm... I'm giving the point to Kirby all the way, because he got the more accurate answer... Scores 1st. wolfman2000-5 points 2nd. NSNick-2 points 3rd. Heian-794-1 point 3rd. Emptyeye-1 point 3rd. Kirby all the way-1 point 4th. Grey-0 points 4th. Teddylot-0 points Another, more difficult geometry question. Question 11 (1 point)- A cone has a radius of 6, and a slant height of 10. Find the volume and surface area. |
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Grey the Stampede Don't mess with powers you don't understand. And yes. That means donuts. Level: 82 Posts: 25/3770 EXP: 5192909 For next: 16318 Since: 06-17-04 From: Kingston, RI, USA, Earth Since last post: 2 hours Last activity: 1 hour |
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| Ugh, cones...... Alright, Volume of a cone is 1/3 Pi*(R^2)(H). I'll assume it's a right circular cone, so to find the actual height we use the pythagorean theorum: 100 = 36+x, X = 64, so the height is 8. So we have 1/3*3.14(since apparently I can't use the more precise version of pi and instead have to use KirbyATW's definition of 3.14) *36*8. The end result is 376.99 Cubic inches. Surface area, as always, pisses me off. The formula, as I learned it, is (pi)(R)(R+(R^2+H^2)^.5). that comes out to 301.44 square inches. A simpler form of the same formula would be (pi)(R)(R+slant height), which gives the same basic answer. Now keep in mind this is using pi = 3.14 not pi = area of a circle divided by its circumference, since Kirby ATW got the point for doing it with that number. (edited by Grey on 06-22-04 09:37 PM) (edited by Grey on 06-22-04 09:37 PM) (edited by Grey on 06-22-04 09:39 PM) |
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JJ64 Boo Level: 45 Posts: 512/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| The point goes to Grey. However, the simplified formula is (pi)(r^2)+(pi)(r)(s). Scores 1st. wolfman2000-5 points 2nd. NSNick-2 points 3rd. Heian-794-1 point 3rd. Emptyeye-1 point 3rd. Kirby all the way-1 point 3rd. Grey-1 point 4th. Teddylot-0 points It's early in the morning, so I'm making it easy... Question 12 (1 point)- Find the equation of the line with the point (4,5) and (-5,-13). |
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Grey the Stampede Don't mess with powers you don't understand. And yes. That means donuts. Level: 82 Posts: 34/3770 EXP: 5192909 For next: 16318 Since: 06-17-04 From: Kingston, RI, USA, Earth Since last post: 2 hours Last activity: 1 hour |
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| Since the line goes up 18 units and over 9 to the right, the slope is 18/9, or 2. Following this through from -5,-13 we can see that the line passes through the Y axis at 0,-3, making that the Y intercept. In slope-intercept form, that makes the formula Y = 2x - 3. (edited by Grey on 06-23-04 09:47 AM) |
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JJ64 Boo Level: 45 Posts: 514/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| And Grey takes the point... Scores 1st. wolfman2000-5 points 2nd. NSNick-2 points 2nd. Grey-2 points 3rd. Heian-794-1 point 3rd. Emptyeye-1 point 3rd. Kirby all the way-1 point 4th. Teddylot-0 points Halfway through round 1... Question 13 (1 point)- Group 1 goes to the beach 4 times a week. Group 2 goes to the week 40 times a year. Group 3 goes to the beach the median of groups 1 and 2. How many times do they all go to the beach combined? |
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KATW King Yoshi "If you stare at something long enough, it can be funny." Level: 86 Posts: 965/3959 EXP: 6087979 For next: 54128 Since: 03-15-04 Since last post: 7 hours Last activity: 5 hours |
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| Okay... 4 times a week is 209 times a year 40 times a year 249/2=124.5 add em all up, and we have.... 373.5 times a year  Is this a leap year we are talking about? |
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JJ64 Boo Level: 45 Posts: 515/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| It's a very special leap year, isn't it? Anyway... Kirby all the way leaps into 2nd... Scores 1st. wolfman2000-5 points 2nd. NSNick-2 points 2nd. Grey-2 points 2nd. Kirby all the way-2 points 3rd. Heian-794-1 point 3rd. Emptyeye-1 point 4th. Teddylot-0 points Yay, a harder one! Question 14 (1 point)- There are 5 cone-shapped seashells on a beach. There are 15 cylinder-shaped shells. The other 45 are hemispheres without a base(a fairly barren beach, eh?). The radius of all the shells are 2. Find the area of all the shells. (edited by JJ64 on 06-24-04 11:30 AM) |
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Grey the Stampede Don't mess with powers you don't understand. And yes. That means donuts. Level: 82 Posts: 41/3770 EXP: 5192909 For next: 16318 Since: 06-17-04 From: Kingston, RI, USA, Earth Since last post: 2 hours Last activity: 1 hour |
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| Shit.... tough one, primarily cause I don't have a height anywhere here. Also, you're saying area, but the thing is these are three dimensional objects and those don't really have an area, they have a surface area. My guess is that you're throwing a curve ball, especially since there's no height or slant height to work with on the cones. But if you're talking surface area, I'll do that. Surface area of a sphere is 4(pi)R^2. Divide that by two, and subtract piR^2 because the bases are missing, and you get 12.556. Multiply that by 45 and you get 565.48 square whatever the units are. Cylinders are 2(pi)R^2, or 25.13 units squared. That, times 15, is 376.99 units squared. Cones are tough... I'm stumped on that one. Best I can do is just plain old (pi)R^2, cause you didn't give me a cone height. In that case, it'd be 12.566 units^2 again, but you'd multiply that one by 5 and get 62.83 total units^2. All of those added together make 1005.301 units^2. I can't think of any other way to do it. |
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Heian-794 Red Super Koopa Level: 44 Posts: 136/896 EXP: 611014 For next: 271 Since: 06-01-04 From: Kyoto, Japan Since last post: 21 days Last activity: 10 days |
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| If you're talking about the area of beach covered under the shells, the heights, etc., would be irrelevant, and the answer would be: 65 x (π x 2^2) = 260π ~= 816.816 What a nifty-looking number! Does it have some significance? |
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JJ64 Boo Level: 45 Posts: 517/919 EXP: 640956 For next: 19208 Since: 05-22-04 From: Green Bay, WI Since last post: 441 days Last activity: 269 days |
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| Grey... you actually can't find the area of all the shells, but you can find the area of the beach under it. I had to add some twist. Anyway, Heian-794 gets the point. Scores 1st. wolfman2000-5 points 2nd. NSNick-2 points 2nd. Grey-2 points 2nd. Kirby all the way-2 points 2nd. Heian-794-2 points 3rd. Emptyeye-1 point 4th. Teddylot-0 points Question 15 (1 point)- Find the cubic root of the square root of (8 |
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