Four cubes of ice with an edge 4 cm each are left to melt in a cylindrical glass with a radius of 6 cm. How high will the water rise when they have melted?

Question

 Mathematics Syllabus D1.

Answer 1

Apparently, they want you to assume that the volume of the ice equals the volume of the liquid water.  That is not strictly correct, because ice has a larger volume that liquid water, for the same amount of water.  (That is why ice floats on liquid water.)  But there is no other way to answer the question, so here goes:

 

Volume of 4 cubes of ice:

 

V = 4(4 cm)³ = 256 cm³

 

When melted, V will fill a volume of height h in the cylinder.

 

V = πr²h ⇒

 

h = V/(πr²) = (256 cm³) / [π(6 cm)²] = ? cm

 

You can finish from here.