Question

Remi has two cone-shaped containers with the same diameter. He will place the smaller container inside the larger one. Before he does this, he wants to fill the larger container with water so that it will be completely full but won’t spill when he places the smaller container inside. The diameter of both containers is 12 cm. The height of the smaller container is 6 cm, and the height of the larger container is 18 cm. What volume of water must Remi put in the large container? Use 3.14 to approximate pi and express your final answer in hundredths. cm3 Diagram showing shorter cone inside taller cone. Both cones share same base, which is fourteen centimeters across. A perpendicular dotted line from middle of base to the point of the shorter cone is labeled three centimeters. A perpendicular dotted line from edge of base to a point level with the point of the taller cone is labeled seventeen centimeters.

Answer 1

Given:
Big cone     : diameter = 12 cm ; height = 18 cm ; base = 14 cm
Small cone: diameter = 12 cm ; height = 6 cm ; base = 14 cm

Volume of a cone-shaped container = π r² h/3
Big cone:
V = 3.14 * (6cm)² * 18cm/3
V = 3.14 * 36cm² * 6cm
V = 678.24 cm³

Small cone:
V = 3.14 * (6cm)² * 6cm/3
V = 3.14 * 36cm² * 2cm
V = 226.08 cm³

Big cone - small cone = volume of water
678.24 cm³ - 226.08 cm³ = 452.16 cm³