Question

Three solid metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted
together and formed into a single cube. Find the volume of new cube.​

Answer 1

$for \: cube \: 1 \\ l = 6 \: cm \\ v_{1} = {l}^{3} = {6}^{3} = 216 \: {cm}^{3} \\ \\ for \: cube \: 2 \\ l = 8 \: cm \\ v_{2} = {l}^{3} = {8}^{3} = 512 \: {cm}^{3} \\ \\ for \: cube \: 3 \\ l = 10 \: cm \\ v_{3} = {l}^{3} = {10}^{3} = 1000 \\ \\volume \: of \: the \: formed \: cube \\ v = v_{1} + v_{2} + v_{3} \\ v = (216 + 512 + 1000) \: {cm}^{3} \\ v = 1728 \: {cm}^{3}$

Hence, volume of the new cube is 1728 cm³

Answer 2

Step-by-step explanation:

\begin{gathered}for \: cube \: 1 \\ l = 6 \: cm \\ v_{1} = {l}^{3} = {6}^{3} = 216 \: {cm}^{3} \\ \\ for \: cube \: 2 \\ l = 8 \: cm \\ v_{2} = {l}^{3} = {8}^{3} = 512 \: {cm}^{3} \\ \\ for \: cube \: 3 \\ l = 10 \: cm \\ v_{3} = {l}^{3} = {10}^{3} = 1000 \\ \\volume \: of \: the \: formed \: cube \\ v = v_{1} + v_{2} + v_{3} \\ v = (216 + 512 + 1000) \: {cm}^{3} \\ v = 1728 \: {cm}^{3}\end{gathered}

forcube1

l=6cm

v

1

=l

3

=6

3

=216cm

3

forcube2

l=8cm

v

2

=l

3

=8

3

=512cm

3

forcube3

l=10cm

v

3

=l

3

=10

3

=1000

volumeoftheformedcube

v=v

1

+v

2

+v

3

v=(216+512+1000)cm

3

v=1728cm

3

Hence, volume of the new cube is 1728 cm³