what is the difference between the volume of the cone, including the shell, and the volume of the ice cream you can fit inside the shell?

Question

An ice cream cone has height 4 in. and radius 1 in. If the cone is 0.1 in. thick, what is the difference between the volume of the cone, including the shell, and the volume of the ice cream you can fit inside the shell?

Answer 1

For a cone, the volume, V, is given by:

V = ∏r²h/3

Note that this is a simple cone, not an "ice cream cone." This cone has a point at one end and it has a circle at the other end. If it has ice cream, then it ends at the circle -- there is not a hemisphere to "top it off."

The problem gives:

r = 1

h = 44∏

thickness is 0.1, so the inside has a radius = 3.9 [0.1 less all around]

The outside volume is:

V_O = ∏(4)²(1)/3

V_O = (16/3)∏

V_O = 5.33∏

The inside volume is:

V_I = ∏(3.9)²(1)/3

V_I = 5.07Π

The difference is:

diff = 5.33∏ - 5.07∏

diff = 0.26∏