The water level in a cylindrical vessel reaches 80 cm. What level will the water reach if it is poured into another

The water level in a cylindrical vessel reaches 80 cm. What level will the water reach if it is poured into another vessel of the same shape, whose base radius is 4 times larger than that of the first.

V (water in the cylinder) = h * pi * R ^ 2

1. Let’s find the volume of water in the first vessel:

V (1) = h (1) * pi * R ^ 2

2. Find the volume of water in the second vessel, where the radius has increased by 4 times:

V (2) = h (2) * pi * (4R) ^ 2

3. Let’s equate the volumes, since of water in the vessel did not decrease, substituting instead of h (1) the value of the water level = 80 cm

V (1) = V (2)

h (1) * pi * R ^ 2 = h (2) * pi * (4R) ^ 2

80 * pi * R ^ 2 = h (2) * pi * 16R ^ 2

h (2) = 5 cm

Answer: 5 cm