If the side of a cube is an integer, which of the following can be the volume of the cube in cubic units?
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Given : side of a cube is an integer,
To find : which of the following can be the volume of the cube in cubic units
1330,1624,1728,1864
Solution:
volume of cube = side³
1330 = 2 * 5 * 7 * 19
1624 = 2 * 2 * 2 * 7 * 29
1728 = 2* 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3
1864 = 2 * 2 * 2 * 233
1728 = 2* 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3
=> 1728 = 2³ * 2³ * 3 ³
=> 1728 = (2 * 2 * 3) ³
=> 1728 = (12) ³
Hence 1728 can be volume of the cube in cubic units
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