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.

828 small spheres can be made from the metal.

Step-by-step 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.

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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