Question

Ram had a cuboid of length is 49 cm, breadth is 49 cm and height is 147 cm. What is the minimum number of such cuboids required to make a perfect cube?

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Answer 1

Step-by-step explanation:

length of cuboid = 49cm

breadth of cuboid = 49cm

height = 147cm

here volume of cuboid = l×b×h

= 49×49×147

= 352947

LCM of L , B and H = 147cm

so volume of cube = s³

= (147)³

= 3176523

so number of cube = volume of cube / volume of cuboid

= 3176523 / 352947

= 9

therefore 9 cube could be formed from the cuboid

Answer 2

Given Question :-

• Ram had a cuboid of length is 49 cm, breadth is 49 cm and height is 147 cm. What is the minimum number of such cuboids required to make a perfect cube?

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$\large\underline\purple{\bold{Solution :- }}$

Dimensions of Cuboid

$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{length \: = 49 \: cm} \\ &\sf{breadth \: = 49 \: cm}\\ &\sf{height \: = 147 \: cm} \end{cases}\end{gathered}\end{gathered}$

$\tt \: Volume, \: V = length \times breadth \times height$

$\tt \: Volume, \: V = 49 \times 49 \times 147$

$\tt \: Volume, \: V = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 3$

$\tt \: Volume, \: V = {7}^{3} \times {7}^{3} \times 3 \: {cm}^{3} - - - (1)$

☆ Let number of cuboids required be 'n' to make it a perfect cube of edge 'x'.

$\tt \: So, \: Volume \: of \: cube \: = \: {x}^{3}$

$\tt \: Hence, \: n \times Volume \: of \: cuboid \: = {x}^{3}$

$\tt\implies \: {x}^{3} = n \times {7}^{3} \times {7}^{3} \times 3$

$\tt \:  ⟼ \: To \: make \: n \times {7}^{3} \times {7}^{3} \times 3 \: a \: perfect \: cube$

$\tt\implies \:n \: = 3 \times 3 \\ \tt\implies \: \: n \: = \: 9 \: \: \: \: \:$

☆ Hence, 9 is the minimum number of such cuboids required to make a perfect cube.

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