A conical vase of base radius 5cm and height 20cm is filled with 200ml of water, how high is the water level? Give your answer to 3 significant figures.

Answer: 2.96 cm

Equations used: Volume of a cone = (base area x height) / 3 ; Base Area = pi x radius²

Volume of whole vase = (pi x 5² x 20)/3 = 523.6 cm³ (4sf) therefore Volume of air in vase with 200ml water = 523.6 - 200 = 323.6 cm³

Since the cone of air is a similar shape to the overall conical vase, height of air = 4 x radius of base. So for air (4 x pi x r³)/3 = 323.6 cm³ -> radius = 4.25 cm & height = 17.04cm, hence the water level is 20cm - 17.04cm = 2.96cm