A uniform ball with a diameter of 3 cm has a mass of 162 grams. What is the mass of a ball made

A uniform ball with a diameter of 3 cm has a mass of 162 grams. What is the mass of a ball made of the same material with a diameter of 2 cm?

The volume of the ball is calculated by the formula: V = (4/3) * π * R³ where V is the volume, π is the number “pi”, R is the radius Let’s calculate the volumes of the first and new balls. 1) V₁ = (4/3) * π * 3³ = (4/3) * π * 27 (cc) 2) V₂ = (4/3) * π * 2³ = (4/3) * π * 8 (cc) Let’s find what part of the volume of the first ball the new ball takes. 3) V₂ / V₁ = ((4/3) * π * 8) / ((4/3) * π * 27) = 8/27 (part) Because balls are made of the same material, then their masses are related in the same way as their volumes. 4) 162 * 8/27 = 48 (grams) mass of the new ball. Answer: 48 grams.