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

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

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.

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%.

Related questions

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

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

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

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.

area is 2, volume is 3

Volume has three dimensions - width, height and depth.

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

The volume doesn't tell the dimensions. It doesn't even tell the shape.

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.

Volume always has three dimensions. Area always has two dimensions. Length always has one dimension. Location has no dimensions.

When we have the dimensions we can find the volume and mass=density*volume

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