Question

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm arc melted :
formed into a single cube. Find the edge of the cube so formed.​

Answer 1

Answer:

volume of three cubes = volume of large cube

Step-by-step explanation:

3^3+4^3+5^3 = x^3

x^3= 27+64+125

x^3 = 216

x= 6.

Answer 2

$\large{\underline{\rm{\blue{\bf{Given:-}}}}}$

Side of first cube = 3 cm

Side of second cube = 4 cm

Side of third cube = 5 cm

$\large{\underline{\rm{\blue{\bf{To \: Find:-}}}}}$

Find the edge of the cube so formed.​

$\large{\underline{\rm{\blue{\bf{Solution:-}}}}}$

We know that,

Volume of cube = $\sf a^{3}$, where a = side of cube

According to the question,

Side of first cube, $\sf a_1$ = 3 cm

Side of second cube, $\sf a_2$ = 4 cm

Side of third cube, $\sf a_3$ = 5 cm

Let us assume that the side of cube recast from melting these cubes = a

We know that the total volume of the 3 cubes will be the same as the volume of the newly formed cube,

Volume of new cube = (Volume of 1st + 2nd + 3rd cube)

$\implies \sf a^{3}={a_1}^{3}+{a_2}^{3}+{a_3}^{3}$

$\implies \sf a^{3}=(3)^{3}+(4)^{3}+(5)^{3}$

$\implies \sf a^{3} = 27 + 64 + 125 = 216$

$\implies \sf a = 6 \: cm$

Therefore, side of cube so formed is 6 cm.