The answer is 249.63 cm³ of water.
1. Calculate the volume of a cylindrical drinking glass (V1).
2. Calculate the volume of spherical pieces of ice (V2).
3. Subtract the volume of the glass and the volume of 25 spherical pieces of ice to get the volume of the water necessary to fill the glass to the rim (V = V1 - 25V2).
1. Volume of the cylinder (V1) is:
V1 = π · r² h (r - radius, h - height)
It is given:
r = 4 cm
h = 12 cm
V1 = π · 4² · 12 = 3.14 · 16 · 12 = 602.88 cm³
2. The volume of the sphere is:
V2 = 4/3 · π · r³ (r - radius)
It is given:
D = 3 cm = 2r
⇒ r = 3 cm ÷ 2 = 1.5 cm
V2 = 4/3 · π · 1.5³ = 4/3 · 3.14 · 3.375 = 14.13 cm³
3. The volume of the glass is V1 = 602.88 cm³.
The volume of one piece of ice is V2 = 14.13 cm³
But since there are 25 pieces of ice, the volume of the water will be:
V = V1 - 25 · V2 = 602.88 - 25 · 14.13 = 602.88 - 353.25 = 249.63 cm³