Q: What are the lengths of the exterior and interior diagonals of a cube that has a volume of 512 cubic cm?

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A rhombus has four equal sides and its diagonals bisect each other at right angles. The area of the rhombus ia given by following formula where x and y are the lengths of the diagonals of the rhombus...A=1/2xy. Example, the diagonals of a rhombus where x = 26 and y = 14....A=1/2xy...=1/2 x 26 x 14 which equals 182. so the area of the rhombus is 182 square inches, miles or whatever measurement you are dealing with the 3d annaloge to a rhombus is the rhomboid, the formula to fin dteh volume of that is A . (B x C).

With 10 cm side lengths, this cube has a volume of 1000 cm3

3.634 cm

not possible

None exist. A square is a measurement of area, length is a linear measurement and volume is a capacity. To find the lengths of a square from the area, take the square root of the area. To find the lengths of a cube from the volume, take the cube root of the volume. To clarify: Area refers to a two-dimensional space. Volume is three dimensional, and thus appropriate for a cube or ball, not a square or circle.

Related questions

It has 0 volume diagonals and 6 face diagonals hence the total number of diagonals are 6

If its base diagonals are 8 and 6 then by using Pythagoras it will have 4 equal lengths of 5 cm. Check: 0.5*8*6*1/3*5 = 40 cubic cm

For the exterior you measure the lenght, width and height - in feet - and multiply them together. To measure the interior volume you will need to measure the diameter of the drum and its depth, in feet. Then volume = 1/4*pi*diameter2*depth.

Take the cube root of the volume.

Multiplication is commutative. To find the volume, you will be multiplying the side lengths together. It doesn't matter what order they are in.

The answer depends on how many there are and the lengths of their sides.

A rhombus has four equal sides and its diagonals bisect each other at right angles. The area of the rhombus ia given by following formula where x and y are the lengths of the diagonals of the rhombus...A=1/2xy. Example, the diagonals of a rhombus where x = 26 and y = 14....A=1/2xy...=1/2 x 26 x 14 which equals 182. so the area of the rhombus is 182 square inches, miles or whatever measurement you are dealing with the 3d annaloge to a rhombus is the rhomboid, the formula to fin dteh volume of that is A . (B x C).

It depends on what dimension(s) of the pentagonal prism are changing. If none then you have only one data point and so nothing to graph. The number of measures that can vary [the degrees of freedom] will range from 2 (for a regular pentagon) to 8 for an irregular pentagonal prism (5 sides of pentagon, 2 diagonals and the length). The reason to include the diagonals is that the lengths of the five sides alone do not uniquely determine the shape of the pentagon and so the volume of the prism. So, in the case of an irregular pentagonal prism, you will need to plot the volume in 9 dimensional space. Have fun!

With 10 cm side lengths, this cube has a volume of 1000 cm3

3.634 cm

not possible

To a certain extent you can. You can look at a Lincoln Town Car and know this is a full sized car. You can look at a Ford Focus and know this is a compact car. But the size of a car is not based on exterior dimensions. It is based on interior dimensions. The EPA, defines market segments by passenger and cargo space. For instance a Mid-Sized car today has between 110 cubic feet and 119 cubic feet of interior volume. Some cars will fool you if you just look at the exterior. It is the interior that counts.