The volume of a cone with diameter d (and hence radius d/2) and height h is
[tex]V_{\rm cone} = \dfrac\pi3 \left(\dfrac d2\right)^2 h[/tex]
so each scoop holds
[tex]V = \dfrac\pi3 \left(\dfrac{1\,\rm in}2\right)^2 \left(2\,\mathrm{in}\right) = \dfrac\pi6 \, \mathrm{in}^3[/tex]
of coffee.
The volume of a cylinder with base diameter d and height h is
[tex]V_{\rm cylinder} = \pi\left(\dfrac d2\right)^2 h[/tex]
so the coffee can contains
[tex]W = \pi \left(\dfrac{6 \, \rm in}2\right)^2 \left(6\dfrac14 \, \mathrm{in}\right) = 2025\pi \,\mathrm{in}^3[/tex]
of coffee.
One full scoop then uses up [tex]\frac VW = \frac1{12,150}[/tex] of the total amount of coffee in the can, so you can make 12,150 cups of coffee.
