Question

the dimensions of a cuboid are 3cm×7cm×3cm. How many such identical cuboids are required to form a cube?​

Answer 1

Answer:

the correct answer is 63 cuboids.

Answer 2

SOLUTION

GIVEN

The dimensions of a cuboid are 3cm × 7cm × 3cm.

TO DETERMINE

The number of such identical cuboids are required to form a cube

EVALUATION

Here it is given that the dimensions of a cuboid are 3cm × 7cm × 3cm

So volume of the cuboid

= 3cm × 7cm × 3cm

$= \sf{63 \: \: {cm}^{3} }$

Now the length of each edge of cube

= LCM of dimensions of the cube

= LCM of 3cm , 7cm , 3cm

= 3 × 7 cm

= 21 cm

So volume of each cube

$= \sf{ {(21)}^{3} \: \: {cm}^{3} }$

Let N number of identical cuboids are required to form a cube

So by the given condition

$\displaystyle \sf{N \times 63 = {(21)}^{3} }$

$\displaystyle \sf{ \implies \: N = \frac{ {(21)}^{3} }{63} }$

$\displaystyle \sf{ \implies \: N = \frac{ 21 \times 21 \times 21 }{63} }$

$\displaystyle \sf{ \implies \: N = \frac{ 21 \times 21 }{3} }$

$\displaystyle \sf{ \implies \: N = 7 \times 21 }$

$\displaystyle \sf{ \implies \: N = 147 }$

Hence the number of such identical cuboids are required to form a cube = 147

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