Easy geometry problem?

Question

I think I know the answer to this problem, but it seems too simple or something...so I want to make sure...

A rectangular box has volume 15cm^3. If the length, width, and height are doubled, what is the volume of the resulting box?

Thank you!

Answer 1

120 cm³

Here's how to be sure:

Let x be width, y be the length and z be the height. Then xyz = 15 cm³ is the volume.

If we double each measurement, then 2x is the width, 2y is the length and 2z is the height. That means the new volume is (2x)(2y)(2z) = (2)³ xyz = (8)15 cm³ = 120 cm³

Answer 2

If you can't figure out a logical way to solve the problem then try a numerical approach.

So, lets assign values to the rectangular box--something completely arbitrary. 2*3*4 = 24
So if we double each part: (2)*2*(2)*3*(2)*4 = 4*6*8 = 192
192 / 24 = 8

So we have one example where doubling the sides results in eight times the volume. This could be a coincidence. We can either take a second numerical trial, or see if we can prove this with algebra.

L = Length
W = Width
H = Height
V = Volume

Start with the true statement
L*W*H = V

Now put forthe statement in question
2*L*2*W*2*H = V*8

Manipulate the statement
2^3*L*W*H = (L*W*H)*8
2^3 = 8
True!

So let's try another numerical trial just for fun. Lets try 3*4*5 = 60
So if we double each part: (2)*3*(2)*4*(2)*5 = 6*8*10 = 480
480 / 60 = 8 = 2^3

Now this was far more work than you could ever possibly need for such a simple problem, but I wanted to show you how to go about a problem that you have absolutely no clue how to solve.

Best of luck! Oh, and the solution is 120 cm^3.

Answer 3

Multiplying every dimension by 2 multiplies the volume by 2^3, since (2a)(2b)(2c) = 8abc.

8 * 15cm^3 = 120cm^3.

Answer 4

Original box:
Volume=l*w*h
15 in^3= l*w*h

Doubling length, width, and height:
Volume= (2l) (2w) (2h)= 8 (l*w*h)= 8 times the original volume
15*8= 120in^3

Answer 5

After pondering this question for a couple of minutes, i'm getting the ratio of the edges is ?(50/18) = 5/3 Or in case you want ?(18/50) = 3/5 Which I surmise is the similarity ratio, to illustrate the ratio of the lengths of the climate of the two octagons. ------------------- For destiny reference, the area length is sq. inches, frequently written as squarein or in²

Answer 6

120cm^3

Answer 7

take the cubed root of 15 to find l, w, and h.
2.466...
double it...
4.932...
cube it (l * w * h)=
120