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) = \frac\pi3 \left(\frac d2\right)^2 h`

so each scoop holds

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

of coffee.

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

`V_(\rm cylinder) = \pi\left(\frac d2\right)^2 h`

so the coffee can contains

`W = \pi \left(\frac{6 \, \rm in}2\right)^2 \left(6\frac14 \, \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.