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

OR

How many shots each having diameter of 3 cm can be made from a cuboidal lead solid of dimensions

We know that,

Volume of cube = a³,

where a = side of cube

Now,

Side of first cube, a₁ = 3 cm

Side of second cube, a₂ = 4 cm

Side of third cube, a₃ = 5 cm

Now, Let the side of cube recast from melting these cubes is 'a'.

As the volume remains same,

Volume of recast cube = (volume of 1^st + 2^nd + 3^rd cube)

⇒ a³ = a₁³ + a₂³ + a₃³

⇒ a³ = (3)³ + (4)³ + (5)³

⇒ a³ = 27 + 64 + 125 = 216

⇒ a = 6 cm

So, side of cube so formed is 6 cm.

OR

Volume of cuboid = lbh

For cuboidal lead:

Length, l = 9 cm

Breadth, b = 11 cm

Height, h = 12 cm

Volume of lead = 9(11)(12) = 1188 cm³

Volume of sphere

where r = radius of sphere

For spherical shots,

Diameter = 3 cm

Radius, r = 1.5 cm

Volume of one shot

Now,

So, 84 bullets can be made from lead.