A scoop of ice cream, shaped like a sphere with a diameter of 6 cm, is placed in an ice cream cone with diameter 5 cm and height 12 cm. Is the cone big enough to hold all the ice cream if it melts? Explain.

The answer is no.

We need to calculate if the volume of the ice cream is equal or smaller than the volume of the ice cream cone.

The volume of the ice cream (sphere) is

V1 = 4/3 r³ π

d = 6

r = d/2 = 6/2 = 3

V1 = 4/3 * 3³ * 3.14 = 113.04 cm³

The volume of the ice cream cone is:

V2 = 1/3 r² h π

d = 5

r = d/2 = 5/2 = 2.5

h = 12

V2 = 1/3 * 2.5² * 12 * 3.14 = 78.5 cm³

Since the volume of the ice cream (V1) is bigger than the volume of the ice cream cone (V2), the cone is not big enough to hold all the ice cream if it melts