Question

Amit makes a cuboid having sides 3cm, 2cm & 3cm. How many such cuboids will be required to form a cube.​

Answer 1

Hi,

Answer: 12

Explanation:

lcm(3,2,3)=6

Volume of a cuboid=3*2*3=18 (cm³)

Volume of the cube=6³=216 (cm³)

Number of cuboids=216/18=12.

Answer 2

Start with a volume of a cuboid,

`V=abc=3\cdot2\cdot3=18\mathrm{cm^3}`

The side of the cube we need equals to the LCM of the cubiod's sides,

`\mathrm{LCM}(a,b,c)=\mathrm{LCM}(3,2,3)=6`

Now compute the volume of such cube,

`V=\mathrm{LCM}(a,b,c)^3=6^3=216\mathrm{cm^3}`

Divide the volumes to get how many cubiods are in such cube,

`\frac{V_{\mathrm{cube}}}{V_{\mathrm{cubiod}}}=(216)/(18)=\boxed{12}`

Hope this helps :)