The water level in a cylindrical vessel reaches h = 10 cm. What level will the water reach

The water level in a cylindrical vessel reaches h = 10 cm. What level will the water reach if it is poured into another vessel of the same shape, whose base radius is half that of the first?

Given:
Cylinder 1 and 2;
H1 = 10 cm;
R2 = R1 / 2;
H2 =?
Decision:
1) Because Since the vessel has a cylindrical shape, then we apply the formula to find the volume of the cylinder. The volume of the cylinder (V) is equal to the product of the base area (S) and the height (H):
V = Sh = πR ^ 2H;
2) Find the volume of water in the first vessel:
V1 = 2R1 ^ 2H1;
and in the second vessel:
V2 = 2R2 ^ 2H2;
3) Because water of the same volume was poured from the first vessel into the second, then:
V1 = V2;
2R1 ^ 2H1 = 2R2 ^ 2H2;
R1 ^ 2H1 = R2 ^ 2H2;
It follows from the equality that:
H2 = R1 ^ 2H1 / R2 ^ 2;
H2 = R1 ^ 2H1 / (R1 / 2) ^ 2;
H2 = R1 ^ 2H1 / (R1 ^ 2/4);
H2 = R1 ^ 2H1 / (4 / R1 ^ 2);
H2 = 4H1;
If H1 = 10 cm, then H2 = 4H1 = 4 * 10 = 40 (see);
Answer: 40 cm.