Question

parikshit makes a cuboid of plasticine of sides 5cm 2cm 5 cm how many cuboids will he need to form a cube.

please give good answers.
full explanation.
mods also help.please.​

Answer 1

✬ Cuboids = 20 ✬

Step-by-step explanation:

Given:

• Sides of cuboid are 5 , 2 & 5 cm.
• He made a big cube using small cuboids.

To Find:

• How many cuboids will he need to form a cube ?

Solution: In the cuboid we have

• Length = 5 cm
• Breadth = 2 cm
• Height = 5 cm

As we know that

★ Volume of Cuboid = L•B•H ★

$\implies{\rm }$ Volume = 5(2)(5)

$\implies{\rm }$ 50 cm³

[ Now, we have to find LCM of the sides of cuboid to get the side of cube. ]

➟ LCM of 5 , 2 , 5 is 10

So, the side of cube formed will be 10 cm. Now volume of cube

★ Volume of Cube = a³ ★

$\implies{\rm }$ Volume = 10³

$\implies{\rm }$ 1000 cm³

∴ Number of cuboids needed = Vol. of cube/Vol. of cuboid

➼ No. of cuboids = 1000 cm³ / 50 cm³

➼ 20 cuboids

Hence, 20 cuboids will be needed to form a cube.

Answer 2

Cuboids = 20

Given :-

• Sides of Cuboid is 5cm, 2cm and 5cm.

To Find :-

• How many cuboids will he need to form a cube.

Solution :-

• Length of cuboid = 5cm
• Breath of cuboid = 2cm
• Height of cuboid = 5cm.

As we know that,

Volume of cuboid = L × B × H

=> Volume of cuboid = 5 × 2 × 5

=> Volume of cuboid = 50cm³ .

Now, take LCM of cuboid's sides,

=> LCM of 5 , 2 and 5

=> 5 | 5 | 2 | 5

=> 2| 1 | 2 | 1

=> |1 | 1 | 1

=> LCM of 5 , 2 and 5 is 5 × 2 = 10.

Since, Side of cube is 10cm.

We know that,

Volume of cube = side³

=> Volume of cube = (10)³

=> Volume of cube = 1000cm³ .

.°. Number of cuboid needed to form a cube = Volume of cube / Volume of cuboid

=> Number of cuboid needed to form a cube = 1000cm³ / 50cm³

=> Number of cuboid needed to form a cube = 20

Thus, Number of cuboid needed to form a cube is 20.