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If you double dimensions in the x, y and z direction, then the volume will be multiplied by 8 (2x2x2)

Q: How does the volume change when you double the dimensions?

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No, it's not that simple. the volume of a box, if let us say (for simplicity's sake) it is cubical in shape, is the length cubed (or if it is rectangular, it is length x width x height). So let us say we have a cubical box 2' on an edge. Its volume is 2x2x2=8 cubic feet. Now let us say that we double the length of an edge. Now we have 4x4x4=64 cubic feet. It has eight times the volume of the smaller box. If we are dealing with a rectangular box rather than a cubical box, the calculations are more complicated, but it remains true that the volume grows much faster than the linear dimensions.

if all 3 dimensions increase b factor of 7 then volume changes by 7 cubed or a factor of 343

area is 2, volume is 3

Volume has three dimensions - width, height and depth.

A 3-Dimensional box's volume will double for each dimension that is doubled. i.e. if just the height, length or depth are doubled, the volume increases 200%, if 2 of those dimensions are doubled the volume increases by 400%. if all 3 are double the volume increases by 800%.

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If you double the cross-sectional area and halve the length, you will still have the same volume but the dimensions will be different.

No, it's not that simple. the volume of a box, if let us say (for simplicity's sake) it is cubical in shape, is the length cubed (or if it is rectangular, it is length x width x height). So let us say we have a cubical box 2' on an edge. Its volume is 2x2x2=8 cubic feet. Now let us say that we double the length of an edge. Now we have 4x4x4=64 cubic feet. It has eight times the volume of the smaller box. If we are dealing with a rectangular box rather than a cubical box, the calculations are more complicated, but it remains true that the volume grows much faster than the linear dimensions.

if all 3 dimensions increase b factor of 7 then volume changes by 7 cubed or a factor of 343

If the other dimensions (length and height) are left unchanged, doubling the width will double the volume.

The dimensions of a cuboid cannot be determined from its volume. You could, for example, double the length and halve the width: that would leave the volume unchanged but the dimensions will be different.

You can't tell the dimensions of a rectangle from its area, or the dimensions of a prism from its volume.

area is 2, volume is 3

Volume has three dimensions - width, height and depth.

A 3-Dimensional box's volume will double for each dimension that is doubled. i.e. if just the height, length or depth are doubled, the volume increases 200%, if 2 of those dimensions are doubled the volume increases by 400%. if all 3 are double the volume increases by 800%.

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For a box, the dimensions the define a volume would be:Height, Width, and DepthFor a cylinder, the dimensions that define a volume would be:Height and Diameter

If only the length is changed and all other dimensions left unchanged, the volume will also triple.