A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Consider eight two-cubic centimeter (2 cm3) sugar cubes stacked so that they form a single 2 x 2 x 2 cube. How does the surface area of the single, large cube compare to the total surface area of the individual eight cubes? Report your answer as a ratio. Be sure to show all calculations leading to an answer

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Preetha hey can you help me please

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @perl hey can you please help

  3. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1433804514862:dw|

  4. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Since your answer is a ratio, you don't need to know the specific surface area of each cube. You just need to know how they compare.

  5. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Look at the small cube to the right. As any cube, it has six congruent square faces. Let's call the area of each face x. What is the total surface area of the small cube?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    12cm^3

  7. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    No. 2 cm^3 is the volume of the small cube. We are not interested in that. Above, I told to let x be the area of 1 face of the small cube. The cube has 6 faces, all congruent squares. If 1 of those faces has an area of x, what is the area of the 6 faces combined?

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohh wait sorry my bad that was me completley overlooking the problem haha

  9. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Once again, if one face of a cube has area x, what is the area of all 6 sides added together?

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6x

  11. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Great. Now we need to look at the large cube on the left in the figure above.

  12. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Since the large cube is made up of 8 small cubes, each face of the large cube is made up of 4 faces of the small cube, right?

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i should probably mention this is physics in case that matters

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and yes that is correct

  15. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1433805366040:dw|

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    24x

  17. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok. See the new figure above. One face of the small cube has area x. One face of the alrge cube has area?

  18. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ^large

  19. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I see. You're ahead of me. Correct. Each face of the large cube has area 4x, and the entire cube has a total surface area of 24x.

  20. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    We now have: Surface area of the small cube: 6x Surface area of the large cube: 24x Now express the ratio of the area of large cube to the area of the small cube using 24x and 6x.

  21. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Fill in the second fraction: |dw:1433805590790:dw|

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6:24, 1:4

  23. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    That is small to large. I would do large to small. |dw:1433805771579:dw| The ratio of the large cube's area tot eh small cube's area is 4:1

  24. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ^to the

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so is that all that needs be done

  26. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yes. The business about 2 cm^3 volume is too much info to throw you off.

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok lol well thank you

  28. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Now I would just like to make an observation. We worked with areas. Now let's look at volumes.

  29. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The small cube has a volume of 2 cm^3. The large cube is made up of 8 small cubes, so its volume is 8 * 2 cm^3 = 16 cm^3, right?

  30. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Also, notice that the side of the large cube is twice the side of the small cube.

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i have a question

  32. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    When the side of the cube was doubled, the area became 4 times larger, and the volume became 8 times larger.

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no i understand that what i don't it how you can tell whether 2cm was the surface area or the volume

  34. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Notice that 4 is 2^2, and 8 is 2^3. This is a general rule helps to know: If a solid changes in size by a scale factor of k, the area changes by k^2, and the volume changes by k^3.

  35. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    A centimeter is a unit of length. Think of a centimeter as being used the same as an inch.

  36. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    A centimeter is smaller than an inch, but both a centimeter and an inch are units of length.

  37. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    excatly and volum is a measure of the area of the entire space a object takes up which i didnt think could be measured by length

  38. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    For example, a regular piece of paper measures 8.5 inches by 11 inches. The length and width are measured in inches. That means the length and width can also be measured in cm.

  39. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    An area is the size of a surface. If you measure a length and width in inches, then the unit of are is the square inch, or sq in., or in.^2.

  40. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    If you measure length and width in cm, then the area is in cm^2, or square centimeters.

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    like yes volume is length time width times hight but seeing as how we only have 2cm^3 shouldnt that be the surface area of a side

  42. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    This is where this problem gets tricky. We were never told the side of the cube. We were only told the volume of the small cube is 2 cm^3. Since length, width, and height are all measured in cm (or inches), when you multiply the length, the width, and the height of a cube together to find the volume, you are multiplying three lengths in cm. You get the units of cm^3.

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i have to go eat can we pick this up in 30 minutes

  44. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The fact they told us the cube was 2 cm^3 means that must be a volume. The units of cm^3 are a giveaway that this measurement of 2 cm^3 must be a volume.

  45. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    The reason I call the problem tricky is that the volume was never needed. Since we were only looking for a ratio of areas, the volume was unnecessary. On top of that, they gave us a volume that you cannot easily show the side as a nice even number. Since a cube has a volume of 2 cm^3, that means the side of the cube is the cubic root of 2 (with cm as the units). \(\large V = 2 ~cm^3\) \(\large side = \sqrt[3]{2~cm^3} = \sqrt[3]{2} ~cm\) The cubic root of 2 is an irrational number that if written as a decimal is a non-terminating, non-repeating decimal. This is why I think the problem is tricky. t gives unnecessary info that is hard to write as a number.

  46. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I also have to go. If you have questions, ask, and I'll try to answer next time I'm on.

  47. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.