Question

Rishi makes a cuboid of sides 5 cm, 2 cm & 5 cm. How many such cuboids will he need to form the smallest cube?

Explain with complete calculations & justifications.

Answer 1

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let
length of smallest cube side be 10 because LCM of sides is 10

volume of cube =10^3
=1000

dimensions of cuboid =5*2*5
volume of cuboid =50

no. of cuboids =1000/50
=20

there fore 20 cubes are required to form
the smallest cube

Answer 2

side of smallest cuboid = LCM of {5,2,5}

= 10 cm

so volume of cube = (a)^3 = (10)^3

= 1000 cm^3

length of cuboid (l)= 5 cm
breadth of cuboid(b)= 2cm
height of cuboid (h)= 5 cm

volume of cuboid =l×b×h

=5×2×5= 50 cm^3

let number of cube required be "n"

so volume of "n" cubes = n×50

so according to question..

=) n×50 = 1000

=) n = 1000/50 = 20 cubes

so number of cubes required = 20ans..

hope it helps...