Can someone please help me with these questions!!!And show work too! Thanks! | Mathematics | Page 1

opaque notch Apr 11, 2024, 8:53 PM

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torn cypressBOT Apr 11, 2024, 8:53 PM

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opaque notch

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graceful cape Apr 11, 2024, 8:55 PM

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opaque notch

Consider it as a difference of two cylinders.
Consider it as a union of a parallelepiped and a triangular prism.
This is just a triangular prism, so you can find its volume directly.

opaque notch Apr 11, 2024, 9:02 PM

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graceful cape 1. Consider it as a difference of two cylinders. 2. Consider it as a union of a ...

Can you give me an answer for the first 2

graceful cape Apr 11, 2024, 9:03 PM

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opaque notch Can you give me an answer for the first 2

What did you get?

opaque notch Apr 11, 2024, 9:04 PM

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I got 2514 cubic meters

graceful cape Apr 11, 2024, 9:05 PM

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opaque notch I got 2514 cubic meters

Almost: you didn't round correctly. Look at how they want you to round the answer.

opaque notch Apr 11, 2024, 9:06 PM

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Wdym? 2514.2?

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Is it 2514.2?

graceful cape Apr 11, 2024, 9:08 PM

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No.

opaque notch Apr 11, 2024, 9:08 PM

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Was I close?

graceful cape Apr 11, 2024, 9:09 PM

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Well, I'm just not sure how you're not getting the right answer. After all, I'm sure you're using a calculator.

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Can you show your process?

opaque notch Apr 11, 2024, 9:09 PM

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Ok

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Volume of the large cylinder: V = PIr^2h r = 7m h = 20m V = 3.14 * (7m)^2 * 20m V = 3079.4 m^3

Volume of smaller cylinder: r = 3m h = 20m V = 3.14 * (3m)^2 * 20m V = 565.2 m^3

Volume of paper = Volumd of large cylinder — Volume of smaller cylinder = 3079.4 m^3 - 565.2 m^3 = 2514.2 m^3

graceful cape Apr 11, 2024, 9:15 PM

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Oh, I see.

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You rounded the intermediate calculations. You shouldn't do that.

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It's better to solve these as usual: introduce the parameters corresponding to what's given, derive the general formula, substitute the values, then round.

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So, for example, suppose in (1) the diameters are d and D and the height is h. Then:
V(roll) = V(outer) - V(inner) = (1/4)πD^2 h - (1/4)πd^2 h = (1/4)π(D^2 - d^2)h

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Now you can substitute the values of d, D and h, and only then you should round.

opaque notch Apr 11, 2024, 9:24 PM

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2520.9

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I’m still so confused

graceful cape Apr 11, 2024, 9:26 PM

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opaque notch 2520.9

Uh, no. Still not sure how you're getting that. We have:
V(roll) = (1/4)π(D^2 - d^2)h = (1/4)π((14 m)^2 - (6 m)^2)*20 m = 800π m^3 ≈ 2513.3 m^3

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Can you show how you got 2520.9 m^3? Just curious.

opaque notch Apr 11, 2024, 9:30 PM

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Volume of outer cylinder:
V(outer) = (1/4) * PI * D^2 * h
V(outer) = (1/4) * 3.14 * (14 m)^2 * 20 m
V(outer) = 3086.12 m^3

Volume of inner cylinder:
V(inner) = (1/4) * PI * d^2 * h
V(inner) = (1/4) * 3.14 * (6 m)^2 * 20 m
V(inner) = 565.2 m^3

Volume of paper:
V(paper) = V(outer) - V(inner)
V(paper) = 3086.12 m^3 - 565.2 m^3
V(paper) = 2520.92 m^3

graceful cape Apr 11, 2024, 9:32 PM

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Again, you are rounding the intermediate calculations. That is not the correct way to solve problems.

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As I said above, the general algorithm for most math/physics/chemistry problems like this is:

Introduce some parameters.
Derive the general formula.
Substitute the values to get the answer.
Round the answer if needed.

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Note that rounding is only done at the very end, and not at any step before.

opaque notch Apr 11, 2024, 9:39 PM

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I think I got it, can we move on to the next question

graceful cape Apr 11, 2024, 9:43 PM

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Sure!

opaque notch Apr 11, 2024, 9:45 PM

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21000 cm^3

graceful cape Apr 11, 2024, 9:45 PM

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You can denote the parameters like this, for example.

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Ah, alright, one sec.

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Hm, no. I'm getting a different answer.

opaque notch Apr 11, 2024, 9:48 PM

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What are you getting

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I need to know if I’m close or not

graceful cape Apr 11, 2024, 9:49 PM

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I'm getting 19800 cm^3.

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What volume did you get in terms of a, b, c and h?

opaque notch Apr 11, 2024, 9:52 PM

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Together?

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Or separately

graceful cape Apr 11, 2024, 9:52 PM

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What do you mean?

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Of course, the final answer will contain all these parameters.

opaque notch Apr 11, 2024, 9:55 PM

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This? Total volume = abc + (1/2)bhc or this?

Length of rectangular prism = a
Width of rectangular prism = b
Height of rectangular prism = c
Height of triangular prism = h

graceful cape Apr 11, 2024, 9:56 PM

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opaque notch This? Total volume = abc + (1/2)bhc or this? - Length of rectangular prism = a ...

abc is correct, but (1/2)bhc isn't quite correct.

opaque notch Apr 11, 2024, 9:58 PM

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Can you just lmk the answers, I need to sleep, I got school tmmr 😭😭😭

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My bad for rushing but I need to sleep

graceful cape Apr 11, 2024, 9:59 PM

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opaque notch Can you just lmk the answers, I need to sleep, I got school tmmr 😭😭😭

Sorry, no. I also want to go to sleep.

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We don't just give away answers here.

opaque notch Apr 11, 2024, 10:00 PM

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Why is that a rule

graceful cape Apr 11, 2024, 10:01 PM

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opaque notch Why is that a rule

To prevent cheating.

opaque notch Apr 11, 2024, 10:02 PM

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graceful cape To prevent cheating.

Wouldn’t that make it easier?

#Can someone please help me with these questions!!!And show work too! Thanks!