#### Question

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

#### Solution

Let the length of each edge of the new cube be a cm

Then,

`a^3=(6^3+8^3+10^3)cm^3`

`⇒ a^3= 1728`

`⇒ a = 12`

∴ Volume of new cube=`=a^3=1728cm^3`

Surface area of the new cube `6a^2=6xx12^2cm^2`

`= 864 cm^2`

Diagonals of the new cube = `sqrt(3a)= 12 sqrt3cm.`

Is there an error in this question or solution?

Solution Three Metal Cubes with Edges 6 Cm, 8 Cm and 10 Cm Respectively Are Melted Together and Formed into a Single Cube. Find the Volume, Surface Area and Diagonal of the New Cube. Concept: Volume of a Cuboid.