Question

Parikshit makes a cuboid of plasticine of sides $5$ cm, $2$ cm and $5$ cm. How much such cuboids will he need to form a cube?

Answer 1

Here cuboids are joined to form a cube.

So,

Volume of cuboid $\times$ Number of cuboids $=$ Volume of cube

Volume of cuboid

sides are $5,2,5cm$

Length $=5cm$

Breadth $=2cm$

Height $=5cm$

Now,

Volume of cuboid $\times$ Number of cuboids $=$ Volume of cube

$5\times 2\times 5\times$ Number of cuboids $=a^3$

$a^3=5\times 2\times 5\times$ Number of cuboids

Volume of Cube

Let side of cube $=a$

Volume $=sid{e}^3$

$=a^3$

Volume $=Length\times Breath\times Height$

$=5\times 2\times 5$

To form cube on the right

We multiply by $5\times 2\times 2$

Thus, in

$a^3=5\times 2\times 5\times$ Number of cuboids

Putting Number of cuboids $=5\times 2\times 2$

$a^3=5\times 2\times 5\times 5\times 2\times 2$

$a^3=\underset{–}{5\times 5\times 5}\times \underset{–}{2\times 2\times 2}$

Therefore,

Number of cuboids $=5\times 2\times 2=20$