Question

I need help on part c !!!

Answer 1

The volume of a cone with diameter d (and hence radius d/2) and height h is

$V_{\rm cone} = \dfrac\pi3 \left(\dfrac d2\right)^2 h$

so each scoop holds

$V = \dfrac\pi3 \left(\dfrac{1\,\rm in}2\right)^2 \left(2\,\mathrm{in}\right) = \dfrac\pi6 \, \mathrm{in}^3$

of coffee.

The volume of a cylinder with base diameter d and height h is

$V_{\rm cylinder} = \pi\left(\dfrac d2\right)^2 h$

so the coffee can contains

$W = \pi \left(\dfrac{6 \, \rm in}2\right)^2 \left(6\dfrac14 \, \mathrm{in}\right) = 2025\pi \,\mathrm{in}^3$

of coffee.

One full scoop then uses up $\frac VW = \frac1{12,150}$ of the total amount of coffee in the can, so you can make 12,150 cups of coffee.