Question

three metal cubes with edges 6cm 8cm and 10cm respectively are melted together and formed into a single give find the diagonal of the new cube​

Answer 1

Answer:

volume remains same so

volume of new cube = v1+v2+v3

= 6^3+8^3+10^3

=216+512+1000

=1728

now volume of new cube = a^3= 1728

edge of new cube = a= cuberoot of 1728

a= 12

therefore surface area of new cube = 6 a^2

=6×12^2

=6×12×12

=864 square cm

Answer 2

Side of the cubes:-

• 6 cm,
• 8 cm, and
• 10 cm.

We know,

Volume of a cube = s³

∴ Total volume of the cubes:-

(6 cm)³ + (8 cm)³ + (10 cm)³

= 216 cm³ + 512 cm³ + 1000 cm³

= 1728 cm³ (Volume of the cube formed)

Now, let the side of the new cube formed = S

∴ S³ = 1728

⟹ S = ∛1728

⟹ S = ∛(12)³

⟹ S = 12 cm

We know,

Diagonal of a cube = s√3

∴ Diagonal = 12√3 cm.

@Psyclone