Rahul makes a cuboid of plasticine of sides $3 cm\times3 cm\times5 cm$. How many such cuboids will he need to form a cube?
Given :
Rahul makes a cuboid of plasticine of sides 3 cm , 3 cm and 5 cm.
To find :
We have to find the number of cuboids required to form a cube.
Solution :
Volume of a cuboid of height h, length l and breadth is lbh.
This implies,
Volume of the given cuboid $= 3 cm\times3 cm\times5 cm = 45 cm^3.$
The minimum length required to form a cube = LCM of 3,3 and 5 $=3\times5=15.$
Therefore,
Minimum length required to form a cube = 15 cm.
Volume of the cube so formed = $(15 cm)^3=3375 cm^3.$
Number of such cuboids required = $\frac{3375}{45}=75.$
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