Answer:
Yes, it will overflow, because the volume of the scoop of ice cream is higher than the volume of the cone.
Step-by-step explanation:
To know if the cone will overflow when the entire scoop of frozen yogurt melts, we need to compare the volume of the scoop and the volume of the cone: if the volume of the scoop is higher, it will overflow.
The volume of the cone is:
V_cone = (1/3)*pi*r^2*h
Where V_cone is the volume, r is the radius and h is the height. So:
V_cone = (1/3)*pi*2^2*6 = 25.1327 in3
The volume of a sphere is:
V_sphere = (4/3)*pi*r^3
Where V_sphere is the volume and r is the radius. If the diameter is 4, the radius is 4/2 = 2. So:
V_sphere = (4/3)*pi*2^3 = 33.5103 in3
The volume of the sphere is higher, so the cone will overflow.
