Raj makes cuboid of plasticizing of sides 15 cm, 30 cm, 15 cm. How many such cuboids will he need to form a cube?
Given :
Sides of cuboid 15 cm, 30 cm, 15 cm .
To find :
We have to find the number of cuboids required to make a cube.
Solution :
Volume of a cuboid of height h, length l and breadth is lbh.
This implies,
Volume of the given cuboid $= 15 cm \times 30 cm \times 15 cm = 225 \times 30 cm^3 = 6750 cm^3$.
The minimum length required to form a cube $=$ LCM of 15,30 and 15 $=$ 30.
Therefore,
Minimum length required to form a cube $= 30 cm$.
Volume of the cube so formed $= (30 cm)^3 = 27000 cm^3$.
Number of such cuboids required $= \frac{27000 cm^3}{6750 cm^3} = 4$.
Number of such cuboids required to make a cube is 4.
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