Question

The volume V of an ice cream cone is given by V = (2/3)πr³ + (1/3)πr²h, where r is the common radius of the spherical cap and the cone, and h is the height of the cone. What is the formula for the volume of an ice cream cone?

1) V = (2/3)πr³ + (1/3)πr²h
2) V = (2/3)πr³ - (1/3)πr²h
3) V = (2/3)πr³ * (1/3)πr²h
4) V = (2/3)πr³ / (1/3)πr²h

Answer 1

The correct formula for the volume of an ice cream cone is V = (2/3)πr³ + (1/3)πr²h, combining the volumes of a spherical cap and a cone.

Step-by-step explanation:

The volume of an ice cream cone is given by a specific mathematical formula that includes the volume of a sphere (for the ice cream) and the volume of a cone (for the cone). The correct formula for the volume of an ice cream cone is V = (2/3)πr³ + (1/3)πr²h, where 'r' is the radius of both the spherical cap (ice cream) and the base of the cone, and 'h' is the height of the conical part. This formula combines the volume of a spherical cap which is given by (2/3)πr³, derived from the formula for a sphere's volume 4/3πr³, and the volume of a cone which is given by (1/3)πr²h.