Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

missashleyn

The ratio of the heights of two similar rectangular prisms is 2:3. What is the ratio of their lateral areas?

  • one year ago
  • one year ago

  • This Question is Closed
  1. LukeBlueFive
    Best Response
    You've already chosen the best response.
    Medals 0

    The area of two similar rectangles is equal to the square of their ratio. Example: Rectangle A = 2x4, Rectangle B = 3x6. A's Area: 8, B's Area = 18. \[\frac{ 8 }{ 18 } = \frac{ 4 }{ 9 } = \left( \frac{ 2 }{ 3 } \right)^2\]

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

    So what is the ratio of the lateral lines of two similar rectangular prisms with the ratio as 2:3?

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

    8:27 2:5 4:9 1:0.33

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

    The lateral lines of both of the similar rectangles will have a ratio of 4:9, which equals 2:3. For example: Rectangle A = 1x5, Rectangle B = 2x10, Rectangle C = 3x15. Also, the definition of similar rectangles states that two similar rectangles will have the same ratio for both their height and width.

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

    Oh okay so the answer is 4:9?

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

    Yes, sorry for answering the wrong question at first.

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

    It's okay, I'm not good with math. All the numbers confuse me, wanna help me with another one? lol

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

    lol, sure, why not?

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

    Haha, okay as long as you explain how to do it I should be able to get it. I'm not asking you to do it for me :) Part 1: Create and provide the dimensions for two similar figures of your choosing. Part 2: What is the similarity ratio of these figures along with the ratio of their surface area and volume? Part 3: Show your work, either using the actual volumes or using the formula, that the volume ratio is true.

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

    Well, personally, I'd choose two small cubes and run the numbers on them, since that would make the math easier.

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

    So what do I need to do? haha o.O

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

    For the first part, give two pairs of three dimensions (one for each cube) that define the shape (such as 1x1x1). Since all cubes are similar, that part takes care of itself.

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

    You with me so far?

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

    |dw:1352233160153:dw|

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

    like that? lol idk

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

    Pretty much, except since the shapes need volume, they need to be 3D, not 2D. |dw:1352233311609:dw|

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

    Okay so is that part 1? How do I do part 2?

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

    What are the dimensions on the 2 small cubes for part 1?

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

    According to the question, it seems like you choose the dimensions. It seems to be teaching you how the equations and ratios work together.

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

    Hm, I don't know how to do this! I'll have to wait and do it later, I have no idea what I'm supposed to do! haha

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

    Maybe I'm not explaining it well. You just come up with two similar shapes, such as two cubes, give their dimensions, such as 1x1x1, 2x2x2, 3x3x3, etc., state what the ratio between them is (1:2, 1:3, etc.), calculate their surface areas (1, 4, 9, etc.) and volumes (1, 8, 27, etc.), then state those ratios are well.

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

    I just don't know how to do it, I'm more of a visual learner. Let's see.. figure 1: 5 inches long, 2 inches wide, and 4 inches high. figure 2: 10 inches long, 4 inches wide, and 8 inches high. So figure 1 is half the size of figure 2 while figure 2 is 2x the size of figure 1? So the ratio of both figures would be 1:2? or 2:1?

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

    Good example. The ratio depends on which figure you are comparing against the other, so both are correct. Figure 1 would have a ratio of 1:2 compared to figure 2, while figure 2 would have a ratio of 2:1 compared to figure 1.

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

    I still need the area though, so is that l*w*h for each cube? if I'm right then figure 1: 40. and figure 2: 320? AHH this is so hard! lol

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

    How do I find the volume of each cube?

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

    Actually, you've already correctly calculated the volume of each figure.

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

    Volume = l*w*h Area = l*w

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

    See now i'm lost -_-

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

    Volume is for three dimensions, surface area is for two. Your two figures will have three unique surface areas each (5x2, 2x4, and 5x4 for the first figure) since all three dimensions have different values. |dw:1352234802496:dw|

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

    Thankfully, all similar rectangles have the same ratios between all of their surface areas.

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

    Just for reference, I think the ratio of the surface area of two similar shapes is equal to the square of their ratio and the ratio of the volume is equal to the cube of their ratio.

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

    I'm just getting more confused.....

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

    Okay, maybe it'll help if I give an example with units, to show the difference between calculating the surface area and the volume. It should also help explain how you can calculate the various ratios.

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

    Let's say you have two cubes. Cube A is one inch on each side (height, width, and length), while Cube B is 2 inches on each side.

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

    So the Cube A looks like this: |dw:1352257542757:dw| Cube B looks the same, just with 2's on each side.

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

    To calculate the surface area, take any two edges and multiply them together. In this case, that would be: \[1 inch \times 1 inch = 1 inch^2\]

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

    Volume is calculated similarly, but you multiply three sides together. \[1 inch \times 1 inch \times 1 inch = 1 inch^3\]

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

    Surface area should always have squared units, while volume should always have cubed units.

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

    Now for Cube B's calculations, Surface Area: \[2 inch \times 2 inch = 4 inch^2\] Volume: \[2 inch \times 2 inch \times 2 inch = 8 inch^3\]

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

    Now, moving on to ratios, you should just think of them as fractions. Cube A's sides are half the length of Cube B's, therefore, the ratio of Cube A's sides to Cube B's sides is 1:2. Cube A's surface area is a fourth that of Cube B's, so the ratio of Cube A's surface area to Cube B's surface area is 1:4. Cube A's volume is an eight of Cube B's volume, so the ratio of their volumes is 1:8.

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

    As you can see, the ratio of their surface areas is equal to the square of the ratio of their sides. Put another way: \[\frac{1}{4} = \left( \frac{1}{2} \right)^2\] Also, the ratio of their volumes is equal to the cube of the ratio of their sides. Namely: \[\frac{1}{8} = \left( \frac{1}{2} \right)^3\]

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

    Does this make sense? If not, I'd be happy to explain specific points more clearly, if you can tell me what you don't understand.

    • one year ago
    • Attachments:

See more questions >>>

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.