Length - Lead cylinder

[Guest]

A cylindrical piece of lead is 7.5 in. in diameter and weighs 168 lbs. Determine the length of cylinder.

My attempt:

Let l = length of cylinder.

Volume of cylinder - pi x radius squared x height (or length).

3.1416 x 3.25 x 3.25 x l = 168

44.17875l = 168

44.17875l / 44.17875 = 168 / 44.17875

l = 3.80273 = 3.8 in.

Where did I miscalculate ?

[Guest]

A cylindrical piece of lead is 7.5 in. in diameter and weighs 168 lbs. Determine the length of cylinder.

Note....... the question gives the the dimensions...Diameter and weight......Not diameter and volume

Volume of cylinder = pi x radius squared x height (or length).......Note this is the volume.....

3.1416 x 3.25 x 3.25 x l = "168".......you put it equal to the weight

44.17875l = 168.<<..........and this is cu inches on one side and lbs on other

You need to use the density of the lead in your equation to make the units cu inches on both sides.

Weight is in lbs or lbs force due to its mass and gravity. Density is its weight in lbs per cu inch or lbs per cu ft.
So weight = density x volume

[Guest]

44.17875 x .41(cu. in. of lead) = 18.113

168 lbs. x 28.88 (lbs.in cu. in.) = 4851.84

??

[Guest]

you need to get the density of lead.....I think it is 0.41 lbs per cu inch
you need to work out the volume based on the weight of 168 lbs and the density of lead
volume is area x length, so length will be volume divided by area

[Guest]

44.17875 x 0.41(cu. in. of lead) = 18.113

168 / 18.113 = 9.275

L = 9.275 in.

Not sure.

[Guest]

Please reply - thanks.

[Guest]

You need to work logically through the question.....You are not following any of the guidance from the earlier posts....

you need to get the density of lead.....I think it is 0.41 lbs per cu inch....YES...it is 0.41 lbs per cu inch

you need to work out the volume based on the weight of 168 lbs and the density of lead
So from the density you now know that every cu inch of lead weighs 0.41 lbs, and you are told in the question that the lead in the cylinder weighs 168 lbs, so every 0.41 lbs of this 168 lbs will be 1 cu inch of volume......so how many 0.41 lbs are there in 168 lbs...??
Once you find the volume then you can use the formula below to find the length....

volume is area x length, so length will be volume divided by area ...... Area x Length = Volume

[Guest]

I don't understand.

[Guest]

You need to work logically through the question.....You are not following any of the guidance from the earlier posts....

you need to get the density of lead.....I think it is 0.41 lbs per cu inch....YES...it is 0.41 lbs per cu inch

you need to work out the volume based on the weight of 168 lbs and the density of lead
So from the density you now know that every cu inch of lead weighs 0.41 lbs, and you are told in the question that the lead in the cylinder weighs 168 lbs, so every 0.41 lbs of this 168 lbs will be 1 cu inch of volume......so how many 0.41 lbs are there in 168 lbs...??

As an example..... If I want to find how many fives there are in twenty ( how many times does 5 go into 20 ) OR if I have 20 sweets how many groups of 5 do I have.

What you do is use your 5 times tables..... 5 times 4 is 20. OR 20 divided by 5 is 4 times.

So for the lead....we know there is 168 lbs of lead in the cylinder and that each 0.41 lbs is 1 cubic inch of volume. So we need to find out how many 0.41 lbs of lead there is in 168 lbs so as above we would divide 168 lbs by 0.41 ....so... 168 / 0.41 = 410 times. and each time is goes that is a cubic inch so 168 / 0.41 = 410 cubic inches

Once you find the volume then you can use the formula below to find the length....

volume is area x length, so length will be volume divided by area ...... Area x Length = Volume

So.... 3.142 x 3.25 x 3.25 x L = 410 ......and you have to solve for L which is the length of the cylinder

[Guest]

3.1416 x 3.75 x 3.75 x L = 44.17875L cu. in.

168 / 0.41 = 409.75609 = 410 cu. in.

410 / 44.17875 = 9.2804 = 9.28 in.

L = 9.28 in.

[Guest]

Yes, correct.

....Problem solving.......Stepwise Refinement......Break the big problems down into logical steps....Solve each step one at a time....

[Guest]

Thanks.

Just for info I worked the problem in cu. ft. -

3.1416 x 0.3125 (in. to ft.) x 0.3125 = 0.3067 cu. ft.

168 / 707 (lbs. per cu. ft.) = 0.237 cu. ft.

0.237 / 0.3067 = 0.772 ft.

0.772 ft. x 12 in. = 9.264 in.

I have a follow-up question:

I located an abbreviated solution - 7.5 ^ 2 x 0.3223 = 18.129
168 / 18.129 = 9.266 in.

My question - What is the "0.3223" indicate ?

[Guest]

If we consider your abreviated solution....
and consider the dimensional analysis of the last line...

168 is the weight in lbs of the cylinder....dimensions are lbs

After you divide it by 18.129 you get 9.266 inches .....the dimensions are inches.

So the dimensions of 18.129 must be "lbs per inch of cylinder" OR lbs/inch

So the dimensional calculation of the last line is.... (lbs) / (lbs/inch)

Which is same as (lbs) X (inches/lb) ....and the lbs cancel and leave you with inches

So that means the calculation on the line before in your abreviated solution is for the weight in lbs of one inch of cylinder....18.129 lbs.

So if we find the volume of 1 inch of cylinder and multiply by density we get the weight in lbs of 1 inch of cylinder.

Volume of 1 inch = Pi x r^2 x 1 ....OR.... volume of 1 inch = Pi/4 x d^2 x 1 ......we will use the Pi / 4 xd^2 x 1 formula because it matches you abrev. solution.

SO the weight of 1 inch of cylinder is Pi / 4 x d^2 x 1 x 0.41 = d^2 x Pi / 4 x 0.41 = d^2 x 0.322

And for this particular question weight of 1 inch = 7.5^2 x 0.322 = 18.11 lbs

So for the cylinder its weight is 18.11 lbs per inch of length.

So how 18.11 lbs is there in 168 lbs to fins how many inches in length.....divide 168 by 18.11

Length = 168 / 18.11 = 9.277 inches.

PS....I know I have rounding errors or used a slightly different density figure, but working out is same.

[Guest]

"d^2 x Pi / 4 "

I am not clear on this part. Thanks.

[Guest]

r = d/2
so r^2 = (d/2)^2 = d/2 x d/2 = d^2 /2^2 = d^2/4

Area = Pi x r^2 OR because as shown above r^2 = d^2/4 we can say Area = Pi x d^2/4

This is same as Pi/4 x d^2 OR d^2 x Pi/4 ......it is just the expression re-arranged.

[Guest]

I understand now. Thanks again.