A reactangular storage unit has dimensions 1m by 2m by 3m.?

Question

If each linear dimension is increased by the same aoumnt. What increase would result in a new storage unit with a volume 10 times the original?

Answer 1

The volume of a rectangular storage unit is given by:
V = W x H x L

In your case, the original volume is:
1 x 2 x 3 = 6 cubic meters

Now you want to increase each dimension by the same amount and get a volume that is 10 times the original.
(1+n) x (2+n) x (3+n) = 60 cubic meters

A bit of trial and error will tell you that n = 2 meter to make the dimensions 3m by 4m by 5m = 60 cubic meters.

Or algebraically you need to solve:
(2 + 3n + n²)(3 + n) = 60
6 + 11n + 6n² + n^3 = 60
n^3 + 6n² + 11n - 54 = 0

This factors to:
(n - 2)(n² + 8n + 27) = 0

Solutions are n = 2, and a couple of complex roots, so the correct answer is you increase each dimension by 2 meters (3m x 4m x 5m = 60 cubic meters).

If they instead mean that the dimensions are increased *proportionally* (e.g. doubled, tripled, etc.) the correct answer is that they are all increased by the cube root of 10, or approximately 2.15443469. So the dimensions would be:
2.15443469 x 4.30886938 x 6.46330407 = 6 x cube root(10)^3 = 60

Answer 2

This is a problem about translating English to Math.

The original dimensions

1* 2 * 3 = 6

Original storage volume=6

What increase would result in new storage unit with volume 10 times original. (each dimension is increased by same amount)

(1+x)(2+x)(3+x)=10*6
=60
you can solve the third order polynomial using alegbra or realize that

3*4*5=60

(1+2)(2+2)(3+2)=60

Therefore X=2

Answer 3

Initial volume=1*2*3=6m^3
increased volume=2*4*6=48m^3
Volume has increased by 8 times

Answer 4

volume formula for a rectangulas storage unit

v = L x W x H

v = 1 x 2 x 3 =

v = 6m

The answer is v = 6m

- - - - - - -s-

Answer 5

1X2X3=6
2X3X4=24
Just keep on testing numbers like this.
3X4X5=60
An increase of two of each dimension gets to 60 (6X10).