Find the mass of a ball with a diameter of 2.5 cm if a ball of the same steel with a diameter of 5 cm weighs 64g.

Since the balls are made of the same material, the ratio of their mass to their volume is equal to each other.

m1 / V1 = m2 / V2.

Let’s use the formula for the volume of a ball. V = (4/3) x R ^ 3 x π.

Then:

64 / ((4/3) x 2.5 ^ 3 x π) = m2 / ((4/3) x 1.25 ^ 3 x π).

(64 x 3) / (4 x 2.5 ^ 3 x π) = (m2 x 3) / (4 x 1.253 x π).

19 ^ 2 / 2.53 = (m2 x 3) / 1.253.

m2 x 3 = 192/8.

m2 x 3 = 24.

m2 = 24/3 = 8 gr.

Answer: The mass of a ball with diameters of 2.5 cm is 8 grams.