A container holds 4608 cubic inches of waste. The dimensions of the container are tripled. How many cubic feet of waste does the new container hold?

Question

I got this answer wrong but the site said the answer was 72. I'm confused how this answer was found and why the new container holds less than the old container if the old container's dimensons are tripled.

Answer 1

Note that the volume of the first container is given in cubic inches and the volume of the second is given in CUBIC FEET so you have to convert cubic inches to cubic feet to make a valid comparison. There are 1728 cubic inches in a cubic foot(12x12x12) which equals 2 2/3 cubic feet. If each dimension is then tripled the volume will increase 27 fold (3x3x3)

27 x 2 2/3 =72 cubic feet

Answer 2

(Maybe you just forgot to change from inches to feet?)

When you change ALL dimensions of an object by a factor F, the area of a 2-dimensional object changes by F squared, the volume of a 3-dimensional object changes by F cubed. This is true for ANY shape object as long as ALL dimensions change by the same multiplier, It's easy to show for simple shapes. For complex shapes the math can get messy, but it's still true.

Note that the factor can be less than 1. 0.5, 1/2, 1/3, .0.84

It works the same if an object is shrunk.

This is a 3-D container and the dimensional factor is F=3. The volume increases by a factor of 3³ = 27.

The answer is 4608 x 27 / 12³ = 72

Notes:

The / 12³ converts cubic inches to cubic feet.

Rectangular solid:

V = L*W*H = LWH

Double all dimensions

V=2L*2W*2H = 2³LWH