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Q.

If one liter of water to fill in a cube shaped tin, what are the measurements required of the cube ____cm.

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Detailed Solution

Given that, one litre of water is filled in the cube. We know that the space inside the solid to occupy is known as the volume of the solid. So, the volume of the cube is given byV=1litV
Let the side length of the cube is x cm as shown in below figure.
Question Image

Question Image

Now the volume of the above cube is given by
V=

x^{3} {cm}^{3}

According to the problem the volume is V=1litV=1lit.
∴

x^{3} {cm}^{3} = 1 lit

.
We have the relation between

{cm}^{3}

and litres as 1lit=1000

{cm}^{3}

.
∴

x^{3} {cm}^{3}

=1000

{cm}^{3}

Taking cube root on both sides of the above equation, then we will get
x=10cm
∴ The measurement of the cube is 10 cm.

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