A drinking glass shaped like a cylinder

With a height of 12 cm and a radius of

4 cm. Maeva adds 25 spherical pieces of ice to the glass the pieces of ice each have a diameter of 3 cm

How many cubic centimeters of water can Maeva add to fill the glass to the rim? Use 3.14 to approximate pi and express your answer in hundreths.

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