Checking of this solution (1 Viewer)

[chrissayyy]

Hey guys, was wondering if anyone could check up on this solution of volume for me, know it sounds stupid but just checking haha its a maths assignment
Question:
By taking approiate measurments and carrying out calculations, answer the following question:
Which would hold the most
- A cylinder made form an a4 sheet of paper, rolled so that it is 'tall and thin'

OR

- A cylinder made from an a4 sheet of paper rolled so that it is "short and fat"

Solution for tall and thin:
Dimension of a paper is 210mm x 297mm
and the radius equals circumference/pie
so 210/pie = d
which is 66.85mm (2.dp)
divide this by 1 and the radius is 33.42
Put in the formula v=pie,r^2,h
so pie x 33.42^2 x 297
= 1042.12 mm


Solution for short and fat:
Dimension of paper is 210mm x 297mm
same as above but formula for diameter becomes
297/pie = 94.54
divide by 2 is radius= 47.47
sub into formula
v= pie x 47.27^2 x 210
=1474.15mm

Are these correct?

Also stuck on this question:
Calculate the area of the curved surface of each of your cylinders
What do you notice?
What is the total surface area of each cylinder? With working

Any help would be appreciated

 

[chrissayyy]

bump

 

[Aesytic]

your volumes seem a bit too small...did you mean cubic cm?

as for the questions you're stuck on:
1. if you think about it, the curved surface is basically your sheet of paper, so therefore its area is the dimensions of your piece of paper, and if you used the same piece of paper for both cylinders...
2. with this one, i'm not sure myself, because the cylinders made would be open at both the top and bottom, so that would mean it'd be the same answer as the first one :/

 

[chrissayyy]

Thanks for replying
yehh there cm3 sorry haha,

Yehh the curved surface area are the same just common sense i didnt have at that time -.- 210x297 = 62370mm2
ohh and for the total surface area theres 'lids' on the bottom anad top

 

[Shadowdude]

1. No, your calculations for the cylinder volume is not correct. Firstly, how can you measure volume (a three-dimensional quality) with millimetres. That's like saying, "Oh, my juice box holds 25cm of liquid". Plus, if you plug in the numbers - say, you did:

pie x 33.42^2 x 297
= 1042.12 mm

When I do that on my calculator, I get 1 042 123.557. When you're doing maths, each step should be logical. Your working should be:

pie x 33.42^2 x 297
= 1 042 123.557
= 1 042 123.56 (to 2 decimal places)

No jumping steps. What I would suggest is to not even simplify, leave it in mm^3 unless you have to convert - because there can be conversion errors.

2. The curved surface of your cylinder is simply the area of your paper you had to begin with.

3. Total surface area of each cylinder is going to be the area of the paper plus 2 times the area of the 'lid' on top. Use A = (pi)(r^2), the area of a circle.

 

[chrissayyy]

Thanks for the feedback!
did it again on the calculator, see where i went wrong, didnt read it properly cause my calculator is ancient and uses comma's so thats where i went wrong haha
is the 'short and fat' cylinder correct?

EDIT: fixed short and fat,
everythings correct I hope.
Thanks for replying guys, will rep