math

2 rectangular prisms are proportional. the edges of the smaller prism are half as long as the edges of the larger prism. The volume of the larger prism is 1,024 cubic feet. the volume of the smaller prism is what?
thank you.

  1. 👍 0
  2. 👎 0
  3. 👁 110
  1. volume proportional to scale ratio cubed
    1/2*1/2*1/2 = 1/8
    so
    1024/8 = 128

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. thank you Damon, but how did you get that equation?

    1. 👍 0
    2. 👎 0
    posted by brianna
  3. Well, you see I am a Naval Architect (ship designer)
    We test ships in model basins
    say the ship is k times as long as the model
    then it is k times as deep
    and it is k times as wide
    so its volume is k * k * k = k^3 times the volume of the model :)
    If you imagine the model to be made up of tiny cubes
    then the ship would have to have k times as many rows along the length
    and k times as many columns in width
    and k times as many high
    so it would need k^3 times the original number of tiny cubes to fill it .

    1. 👍 0
    2. 👎 0
    posted by Damon
  4. i know how to get volume,but i need to know how to find the volume of a prism. this prism is proportional to a smaller prism. but the edges of the smaller prism is half as long as the edges of the larger prism. the volume of the larger prism is 1,024 cubic feet. then the volume of the smaller prism is what? i still do not get it. by the way, that's interestinng that you design ships.

    1. 👍 0
    2. 👎 0
    posted by brianna
  5. are you still there?

    1. 👍 0
    2. 👎 0
    posted by brianna
  6. if the small prism is proportional to the large prism
    Then the height of the small prism is proportional to the height of the large prism
    H = k h
    and the length is also proportional
    L = k l
    and the width is proportional
    W = k w
    so
    L W H = k l * k w * k h = k^3 lwh

    1. 👍 0
    2. 👎 0
    posted by Damon
  7. It does not matter the shape as long as the two objects have the same shape.
    The ratio of their volumes is the scale ratio cubed.
    (by the way the ratio of any equivalent areas on them is the scale ratio squared)

    1. 👍 0
    2. 👎 0
    posted by Damon
  8. That is why I answered your cylinder problem further down the same way. You do not have to know pi.

    1. 👍 0
    2. 👎 0
    posted by Damon
  9. ohhh, now i get where you got that equation from, but how do i find out what thesize of the edges are, and what does k mean?

    1. 👍 0
    2. 👎 0
    posted by brianna
  10. The volume of the small prism is (1/8) times the volume of the large prism.

    1. 👍 0
    2. 👎 0
    posted by Damon
  11. oh, but if the volume of the large prism is 1024, and the edges of the smaller prism is half the length of the larger prism, then what does k mean in your explanation?

    1. 👍 0
    2. 👎 0
    posted by brianna
  12. k is the scale ratio
    in this case every length on the small one is 1/2 the equivalent length on the big one
    so k = 1/2
    and k*k*k = k^3 = 1/8

    1. 👍 0
    2. 👎 0
    posted by Damon
  13. every edge and other length measurement on the little one is 1/2 that on the big one
    so k = 1/2

    1. 👍 0
    2. 👎 0
    posted by Damon
  14. Now I have to do a pretty long statistics problem for Sherri but will check back later.

    1. 👍 0
    2. 👎 0
    posted by Damon
  15. oh, so the length of the small one is 1/8th? but the question says they are rectangular prisms. so they will both have 2 different measurements for the 2 different sixes of the edges

    1. 👍 0
    2. 👎 0
    posted by brianna
  16. ok

    1. 👍 0
    2. 👎 0
    posted by brianna
  17. Damon,im in 8th grade math, and i don't really get what you are saying. because we haven't really talked about a scale ratio is. ill wait 'till you are done with sherri.

    1. 👍 0
    2. 👎 0
    posted by brianna
  18. OK, I am back from the statistics
    Now say we have two cubes
    one is 1 cm on every edge
    so its volume is 1*1*1 = 1 cm^3

    Now another cube (same shape of course)
    But it is 2 cm on an edge
    so its volume is
    2 * 2 * 2 = 8 cm^3
    see what happened?

    1. 👍 0
    2. 👎 0
    posted by Damon
  19. Then what if the second cube were 3 cm on every edge?
    volume = 3 * 3 * 3 = 3^3

    1. 👍 0
    2. 👎 0
    posted by Damon
  20. they are not cubes. they are rectangular prisms. i really sorry if i confused you.

    1. 👍 0
    2. 👎 0
    posted by brianna
  21. Now make it harder
    Let's say the first cube was 3 cm on an edge
    then its volume is
    3*3*3 = 27 cm^3
    Now say the big one is 6 cm on an edge
    its volume is
    6 * 6 * 6 = 216 cm^3
    BUT I would not do that
    I would say
    2*3 * 2*3 * 2*3 = 2^3 * 27 = 8 * 27
    because my scale ratio is 2
    therefore my big volume is 8 times the little one.

    1. 👍 0
    2. 👎 0
    posted by Damon
  22. It does not matter what shape, only that they are the same shape

    1. 👍 0
    2. 👎 0
    posted by Damon
  23. no, they are rectangular prisms, not cubes

    1. 👍 0
    2. 👎 0
    posted by brianna
  24. No matter what shape they are, every height is twice, every width is twice, every length is twice
    so every volume is eight times

    1. 👍 0
    2. 👎 0
    posted by Damon
  25. Does not matter shape, as long as the shape is the same. Only the size changes. The volume changes as the cube of every length measurement change ratio.
    here is a sphere with 2 cm radius:
    vol = (4/3) pi (2^3)
    here is a sphere with 4 cm radius (k = 2)
    vol = (4/3) pi (4)^3
    2^3 = 8
    4^3 = 64
    SEE - twice the radius--> EIGHT times the volume

    1. 👍 0
    2. 👎 0
    posted by Damon
  26. If every length on the big one were three times the little one, then the volume of the big one would be 3*3*3 = 27 times the volume of the little one.

    1. 👍 0
    2. 👎 0
    posted by Damon
  27. so wouldn't i divide the volume of the larger prism(1024 cubic feet) by 8

    1. 👍 0
    2. 👎 0
    posted by brianna
  28. Yes!!
    You got it
    1024 / 8 = 128 !!

    1. 👍 0
    2. 👎 0
    posted by Damon
  29. then i'd divide 1024 and 2, because the smaller one is half as small

    1. 👍 0
    2. 👎 0
    posted by brianna
  30. YES!! ithank you sooooo much! i would have gotten ZAP at school if i didn't finish this homework.
    THANK YOU SOOOO MUCH!!!

    1. 👍 0
    2. 👎 0
    posted by brianna
  31. No, the volume of the little one is 1024 / 8
    The smaller volume is 1/8 times the big one

    1. 👍 0
    2. 👎 0
    posted by Damon
  32. You are welcome - now check that cylinder question down below. Same way.

    1. 👍 0
    2. 👎 0
    posted by Damon
  33. YES !

    1. 👍 0
    2. 👎 0
    posted by Damon
  34. okay,thank you again you are pretty good at this sort of stuff

    1. 👍 0
    2. 👎 0
    posted by brianna
  35. wlecsazvq gunmdv wjxvf cbzpok kuiqtebw tnipx yelzcx

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    The volume of a larger prism is 168 cubic cm. if the prisms are similar with a linear ratio of 3:2 what is the volume of the smaller prism? How do i figure that out? Did you learn that the volumes of similar objects are

    asked by emily on April 29, 2007
  2. Math

    Suppose you have two similar rectangular prisms. The volume of the smaller rectangular prism is 343 in^3 and the volume of the larger rectangular prism is 1,000 in^3. What is the scale factor of the smaller figure to the larger

    asked by SkatingDJ on May 6, 2016
  3. geometry

    the volume of a larger prism is 128 cubic cm. if the prisms are similar with linear ration of 4:3, what is the volume of the smaller prism? We have a theorem that says The volumes of similar objects are proportional to the cubes

    asked by Emily on April 26, 2007
  4. Math

    Which statement is true about all prisms? A. Prisms have a pair of opposite faces B. The faces of a prism are congruent C. Prims have the same number of verticrs as edges D. The base of a prism is larger then the other faces.

    asked by Bill on November 22, 2010
  5. geometry

    Two similar rectangular prisms have a scale factor of 4:9. The volume of the smaller prism is 60 cm3. Find the volume of the larger prism.

    asked by hello on July 16, 2010
  6. geometry

    The ratio of two similar prisms is 2:5 the volume of the larger is 375cm3 if sand is being poured into the smaller prism at 3cm3 per second how many seconds will it tAke to fill the smaller prism?

    asked by Olivia on April 7, 2013
  7. math- check

    please check: this deals with a rectangular prism: RECTANGULAR PRISM HAS (6 FACES) 4 FACES ARE FORMED BY RECTANGLES 2 FACES ARE FORMED BY SQUARES A RECTANGULAR PRISM HAS 12 EDGES A RECTANGULAR PRISM HAS 8 VERTICES t FOR TRUE, f

    asked by Celest on May 21, 2012
  8. Math

    The volume of a rectangular prism is 60 cubic in and the lengths of its edges are all whole numbers. What is the number of inches in the largest possible sum of all of the edges of the prism?

    asked by PT on November 14, 2018
  9. Geometry

    A regular pentagonal solid prism has 9cm base edges. A larger, similar solid prism of the same material has 36cm base edges. How does each indicated measurement for the larger prism compare to the same measurement for the smaller

    asked by George on September 29, 2013
  10. geometry

    two smaller prisms have heights 2' and 10'. If the volume of the smaller prism is 32 cubic feet, find the volume of the larger prism.

    asked by Bill on June 4, 2011

More Similar Questions