Question

the edges of a cube are 6cm,8cm,10cm these cubes are melted and recanted to form a new cube. Find the edge of the resulting cube

Answer 1

Hey if you melt three cubes to make a single cube then the volume of the 3 cube is equal to the volume of the single cube that you have made from the rest

6³+8³+10³=216+512+1000=1728

So 1728 is the volume of the given cube

Hence edge length is cube root of 1728 and it is 12cm

Answer 2

First, we must find the volume of each cube.

Volume of cube with edge 6cm =

6³ cm³ = 216 cm³

Vol. of cube with edge 8cm =

8³ cm³ = 512 cm³

Vol. of cube with edge 10cm =

10³ cm³ = 1000 cm³.

When we recant this, we are adding all the three cubes' volumes. That means, the resultant mass's volume =

216 cm³ + 512 cm³ + 1000 cm³ = 1728cm³

Hence, 1728 cm³ is the volume of the resultant mass.

Now, this is converted to a cube, which means that its height, length , and width are all the same. That is,

l = b = h, and let us say that all equal to 'l'.

Hence, volume = l×l×l = l³ = 1728cm³.

Hence, l = edge of the resultant cube = ³√1728cm³ = 12 cm.

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