Question

Three solid cubes of edges 6 centimetre 10 cm and x cm melted to form a single cube of Edge 12 cm find the value of x

Answer 1

A/q
Vol of 1st cube : a^3=6^3=216
Vol of 2nd cube : 10^3=1000
Vol of 3rd cube : x^3
Vol of larger cube : 12^3=1728
Now, 216+1000+x^3=1728
x^3=1728-216
x^3=512
x=8cm

Answer 2

The volume of First cube

$V1 \: = {6}^{3} = 216cm {}^{3}$

The volume of Second cube

$V2 \: = {10}^{3} = 1000cm {}^{3}$
The volume of Third cube

$V3 \: = (x) {}^{3} = {x}^{3}$

The volume of the Forth ( new single ) cube

$V4 \: = {12}^{3} = 1728$

ATQ

$V1 + V2 + V3 \: = V4 \:$

$= > 216 + 1000 + {x}^{3} = 1728 \\ = > {x}^{3} = 1728 - (1000 + 216) \\ = > {x}^{3} = 1728 \: - 1216 \\ = > {x}^{3} = 512 \\ = > x = \sqrt[3]{512 } \\ = > x = 8$
The value of x is 8