Question

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.

Answer 1

Answer:

The each edge of third smaller cube is 10 cm .

Step-by-step explanation:

Given as ;

A metal cube of edge 12 cm is melted and formed into three smaller cubes.

i.e The each edge of bigger cube = a = 12 cm

The each edge of first smaller cube = b = 6 cm

The each edge of second smaller cube = c = 8 cm

Let The each edge of third smaller cube = d cm

According to question

∵ volume of cube = edge³

A metal cube of edge 12 cm is melted and formed into three smaller cubes = each edge of first smaller cube + each edge of second smaller cube + each edge of third smaller cube

or,  a³  = b³ + c³ + d³

Or, d³  = a³ - b³ - c³

Or, d³  = 12³ - 6³ - 8³

Or, d³  = 1728 - 216 - 512

Or, d³  = 1000

∴   d = ∛1000

i.e   d = 10 cm

So, The each edge of third smaller cube = d  = 10 cm

Hence, The each edge of third smaller cube is 10 cm . Answer

Answer 2

The edge of the third smaller cube is 10 cm

Step-by-step explanation:

• Given data

        Side of large cube (a) =12 cm

        Side of first smaller cube (b) =6 cm

        Side of second smaller cube (c) =8 cm

        Side of third smaller cube = d = unknown

• We know volume of cube $\mathbf{=side^{3}}$

Volume of first smaller cube+Volume of second smaller cube+Volume of third smaller cube =Volume of  large cube

       So

       $\mathbf{b^{3}+c^{3}+d^{3}=a^{3}}$

       $\mathbf{6^{3}+8^{3}+d^{3}=12^{3}}$

       $\mathbf{216+512+d^{3}=1728}$

      $\mathbf{d^{3}=1000}$

      So

      d= 10 cm = This is side of third smaller cube