Q. 43.6( 190 Votes )
Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
Volume of 1 cuboid = 5 x 5 x 2 = 50 cm3
Let the volume of the cube to be formed from given cuboids = x cm3
Now we know that this value x will be a perfect cube
Number of cuboids x Volume of 1 cuboid = Volume of cube
Thus we can see that we have to multiply volume of 1 cuboid such that the resulting number is a perfect cube.
Thus, 50 x (Some number) = Perfect cube
Thus, 2 × 5 × 5 × n is a perfect cube
Now, to make this a perfect cube, minimum value of 'n' should be 2 × 2 × 5 (such that it has 3 factors of 2 and 5 each)
i.e. n = 20
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By taking three different, values of n verify the truth of the following statements:
(i) If n is even, then n3 is also even.
(ii) If n is odd, then n3 is also odd.
(ii) If n leaves remainder 1 when divided by 3, then n3 also leaves 1 as remainder when divided by 3.
(iv) If a natural number n is of the form 3p+2 then n3 also a number of the same type.RD Sharma - Mathematics
Which of the following numbers are not perfect cubes?
(iv) 1728RD Sharma - Mathematics