Answer:
Density will be half of the original density and is equal to 5245 kg/m³
Step-by-step explanation:
Given:
Density of the cube is, [tex]d_{cube}=10,490\textrm{ }kg/m^3[/tex]
Let the side of the cube be [tex]x[/tex] m.
Volume of the cube, [tex]V_{cube}=x^{3}[/tex]
If one side of the cube is doubled, the resulting figure is a cuboid with dimensions [tex]x, x,\textrm{ and }2x[/tex]
So, new volume is, [tex]V_{cuboid}=x\times x\times 2x=2x^{3}[/tex]
Density is given as,
[tex]d=\frac{mass}{volume}[/tex]
If mass is constant, then density is inversely proportional to its volume.
Therefore,
[tex]\frac{d_{cuboid}}{d_{cube}}=\frac{V_{cube}}{V_{cuboid}}\\\frac{d_{cuboid}}{d_{cube}}=\frac{x^{3}}{2x^{3}}\\\frac{d_{cuboid}}{d_{cube}}=\frac{1}{2}\\d_{cuboid}=\frac{1}{2}\times d_{cube}\\d_{cuboid}=\frac{1}{2}\times 10490\\d_{cuboid}=5245\textrm{ }kg/m^{3}[/tex]
So, the density of a constant mass is exactly half the original density when one of its sides is doubled.
