A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

The ratio of the surface areas of two cubes is 49/81 What is the ratio of their volumes?

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

    thats fairly easy

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

    surface area of a cube is 6a^2 , where a is the side length

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so let one cube have side length x, the other have side length y

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 6x^2 / 6y^2 = 49 / 81

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now we want the ratio of volume volume of a cube is a^3

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

    therefore the ratio of volumes is (x^3 / y^3 )

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    from the first equation we know that x^2 / y^2 = 49/81 so (x/y) = +- 7/9 ( by taking sqrts ) , but we are dealing with lengths ( which must be positive, so take the + case

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

    so the ratio of volumes = (x^3/y^3) = (x^2 / y^2 ) times (x/y) = 49/81 x 7/9

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    = 0.471 as a decimal to 3 decimal places

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

    i'm alittle confuse

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    with what ?

  12. dumbcow
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[SA \rightarrow \frac{6a ^{2}}{6b ^{2}} = \frac{a ^{2}}{b ^{2}}=\frac{49}{81}\] \[\sqrt{\frac{a ^{2}}{b^{2}}} = \sqrt{\frac{49}{81}}\] \[\frac{a}{b} = \frac{7}{9}\] \[V \rightarrow \frac{a^{3}}{b^{3}} = \frac{7^{3}}{9^{3}}\]

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

    surface area is area, so it is two dimensional, while volume is three dimensional. (square units vs cubed units) you have a ratio of two squares, 49 and 81 being 7^2 and 9^2. therefore the ratio of the lengths of the sides must be 7 to 9 and the ratio of the volumes must be 7^3 to 9^3. dumbcow(nice handle) said it nicely.

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

    so the ratio is 7:9

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no :|

  16. 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.