Math Is Fun Forum

Titus

Member

Registered: 2005-03-07

Posts: 10

Problem Solving

lets say for example;

I want to make a non-cylindrical water tank which much have a volume of 6m cubed, from a single sheet of metal.

This sheet of metal has an area of 6m squared, but it's too small to make the tank. why is that?

Last edited by Titus (2005-03-29 18:55:13)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Problem Solving

The smallest surface area for the largest volume works out to be a sphere (a ball shape).

We see this easily when we blow up a balloon, or even a plastic bag. The surface doesn't like being stretched, so it forms itself into the shape that has the least surface area to contain all the air we pushed in.

So, assuming we could form the sheet metal into a sphere (cutting and joining very cleverly!), how much volume could we enclose?

Hmmm ... let's work out the radius first ...

The formula for the Area of Sphere is:

A = 4 pi r^2     (4 times pi times radius squared)

Flipping this around so that we can figure radius from area:

r = Sqrt(A/4pi)      (square root of area divided by 4 times pi)

We know that the Area is 6m2, so let's solve:

r = Sqrt(6/4pi) = 0.69 m (using my calculator)

Now, Let's figure out the Volume. The Volume of a Sphere is calculated by:

V = (4/3) pi r^3    (four-thirds times pi times radius cubed)

V = (4/3) pi 0.69^3 = 1.38 m3

So, the best we could do is to create a sphere containing 1.38 m3 -- so 6m2 of sheeting cannot make 6 m3 of volume.

Anyone care to double check my calculations?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Roraborealis

Member

Registered: 2005-03-17

Posts: 1,594

Re: Problem Solving

*edges off into the distance*

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School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Mr T

Member

Registered: 2005-03-30

Posts: 1,012

Re: Problem Solving

i learnded aboot dat in maffs lessons

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I come back stronger than a powered-up Pac-Man
I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large
Fatboy Slim is a Legend

stewie

Member

Registered: 2005-03-28

Posts: 820

Re: Problem Solving

i dont do maffs at school but i do maths

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HAPPY HAPPY, JOY JOY 
Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Mr T

Member

Registered: 2005-03-30

Posts: 1,012

Re: Problem Solving

is it because i is black

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I come back stronger than a powered-up Pac-Man
I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large
Fatboy Slim is a Legend

Zach

Member

Registered: 2005-03-23

Posts: 2,075

Re: Problem Solving

Oh Em Gee! It's the Tiger from 'Kenya' by the People who bought us Weeble and Bob. Elle Oh Elle! Ewe Ar Great!

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Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

Eniara

Guest

Re: Problem Solving

Waht if is :

                  Of the 56 signers of the declartion of independence, only William Ellery was a lawyer & a merchant.  of the rest, 39 were either lawyers or merchants. there we 9 more lawyers than merchants.  The product of the numbers of these careers is 360.  How many lawyers were there?

polylog

Member

Registered: 2006-09-28

Posts: 162

Re: Problem Solving

Of the 56 signers of the declartion of independence, only William Ellery was a lawyer & a merchant.  of the rest, 39 were either lawyers or merchants. there we 9 more lawyers than merchants.  The product of the numbers of these careers is 360.  How many lawyers were there?

let L and M be natural numbers.

L := number of lawyers
M := number of merchants

The relevant data given is: 

L = M + 9  ... (1)

LM = 360   ... (2)

Substitute (9 + M) for L in the second equation:

M^2 + 9M = 360
M^2 + 9M - 360 = 0

Apply the quadratic formula:

M = (-9 +/- 39) / 2

  = 15 or -24

reject -24 since the solution needs natural numbers.

Therefore M = 15

From equation 1:

L = 15 + 9 = 24

So:

There were 15 merchants and 24 lawyers.

Check: 15 + 24 = 39, as stated.