Beer Barrel
A dealer used to sell local beer using a cylindrical barrel of radius 10" and length 40". One day the barrel got broken. He found another barrel of similar dimension, radius was 40" and length 10".
"Wow ! what a coincidence I don't have to buy a new barrel now. I can use this one without changing anything," He thought.
"Wow ! what a coincidence I don't have to buy a new barrel now. I can use this one without changing anything," He thought.
Can he?
Labels: mathemagic
posted by Rajesh Lal at
3:49 AM
11 Comments:
he can use the new barrels but no there will be changes bcuz the old barrels' volume was 12,560 m3 but the new ones' is 502,400 m3 O.o huge difference
No, he cannot.
Volume of a cylinder = (pie x (radius)squared x h)
So, with the first cylinder, his volume was 3.14 x 10 x 10 x 40 = 12560. With the new barrel, it would be 3.14 x 40 x 40 x 10 = 50240
old barrel:
10" radius, 40" length
3.14159265359 * 10^2 * 40 =
12566.37061436 cubic inches.
new barrel:
40" radius, 10" length
3.14159265359 * 40^2 * 10 =
50265.48245744 cubic inches.
new barrel is much larger..
?????????????????????this was the most poorly worded question i have ever read i had to read it twice because i goy so confused.
The volume depends on three factors, height, width and length which are all multiplied together.
In both cases the values are all the same except they have changed from being the height to being the length.
No values have changed so both volumes are the same.
I say nay the volume would be different.
No, he would have 2 change something. Because he sold beer in a barrel and if that barrel broke, the beer would spill out. Even if he finds another barrel, he would still have 2 change something (put more beer in the other barrel)
Yes, he can use that barrel. even though the volumes are different (new barrel is 4 times bigger) he can still store his ~12566 cubic inches of beer in it. As a bonus he can also store an additional 37698 cubic inches of beer in the new barrel as well. Hooray
Nevzat
The new barrel volume is exactly 4 times that of the old barrel, so he can still sell beer, but the customer must order some multiple of 4 times the volume in an order. More beer for everyone! I see nothing wrong with that.
The volume of a cylinder is pi*radius
squared times the height.
v = pi()*r^2*h
original volume = 3.1415 * 10^2 * 40
new volume = 3.1415 * 40^2 * 10
The ratio of the old / new is
=( 100*400) / (1600 *100)
= 4000/ 16000 = 1/4
So the new barrel is 4 times the volume of the old
Boy I sure hope the barrel was empty when he broke it, I bet it was, and he was drunk, thats why he broke it.
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