Explanation:
To determine whether the ice cream scoop will fit in the cone or overflow, we need to compare the volume of the scoop to the volume of the cone. If the volume of the scoop is less than or equal to the volume of the cone, the scoop will fit in the cone. If the volume of the scoop is greater than the volume of the cone, the scoop will overflow.
The formula for the volume of a sphere is:
V_sphere = (4/3)πr³
where r is the radius of the sphere. In this case, the radius of the ice cream scoop is 3 cm, so:
V_sphere = (4/3)π(3 cm)³ ≈ 113.1 cm³
The formula for the volume of a cone is:
V_cone = (1/3)πr²h
where r is the radius of the base of the cone and h is the height of the cone. In this case, the radius of the cone is also 3 cm and the height of the cone is 5 cm, so:
V_cone = (1/3)π(3 cm)²(5 cm) ≈ 47.1 cm³
Therefore, the volume of the ice cream scoop is greater than the volume of the cone, and the ice cream will overflow when it melts.
To explain this result, we can note that the volume of the ice cream scoop is determined by its shape and size, which cannot be changed. However, the volume of the cone is determined by both its shape and size, as well as the amount of space available inside it. When the ice cream melts, it will fill up the cone and displace the air inside, increasing the volume of the cone. However, the volume of the ice cream scoop will not change, so it will overflow the cone.