Question

A metal cube of edge 12cm is melted and formed in to three similar cubes if the edge of two smaller cube is 6 cm and8 cm find the edge of the third smaller cube

Answer 1

Given :

Edge of a bigger cube (R)= 12 m

Edge of a first smaller cube(r²)= 8 m

Edge of a second smaller cube(r2)= 6m

Volume of a cube = side³

Volume of a bigger cube(V) = (sides)³
= (12)³= 1728m³

It is melted into three other cubes ,so the volume of the smaller cubes remains same as the volume of bigger cube .



volume of the first smaller cubes(V1)= (8)³=512m³

volume of second smaller cube(V2) = 6³ = 216m³


Total volume(V) = volume of first smaller cube(V1) + volume of second smaller cube(V2)+ + volume of third smaller cube(V3)

V= V1+V2+V3

1728 = 512 +216+V3

1728 = 728+V3

1728 - 728 = V3

1000 = V3


volume of third cube = 1000 m³

Edge³= 1000

Edge = ³√1000

Edge =³√10×10×10

Edge= 10 m

Hence, the edge of the third cube is = 10m

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Hope This will help you....