Question

A metal cube has sides of length 4.5 cm, correct to the nearest 0.5 cm.

The cube is melted down and the metal is used to make small spheres.
Each sphere has a radius of 3 mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal.

Answer 1

828 small spheres can be made from the metal.

Explanation:

Side of the cube = 4.5cm

Volume = (a x a x a)

= (4.5 x 4.5 x 4.5)

= 91.125 cubic cm

Radius of the sphere = 3mm = 0.3 cm

Volume of 1 sphere = (4/3) π(r x r x r)

= (4/3) (3.14) (0.3 x 0.3 x 0.3)

= (4/3) (3.14) (0.027)

= 0.34/3

= 0.11 cubic cm

No. of spheres = 91.125/0.11

= 828.4

So, 828 small spheres can be made from the metal.