Question

Middle School plans to sell ice cream at a charity event. They expect to sell about 100 scoops of ice cream. The ice cream comes in cylindrical cartons. A carton of ice cream has a radius of 11cm and height of 30 cm. A scoop of ice cream has a radius of 3cm.a. How many cartons of ice cream should Ester order to make 100 scoops?

Answer 1

One carton

Step-by-step explanation

First, we have to find the total volume of ice cream of 100 scoops. Let's assume that the scoops are perfect spheres, whose radius is 3 cm. The volume of each scoop is,

`V_(scoop)=(4)/(3)\pi r^3=(4)/(3)\pi\cdot3^3cm^3=36\pi cm^3`

Now, to find what is the total volume of ice cream in 100 scoops, we have to multiply the volume of one scoop by 100,

`V_(100scoops)=100\cdot36\pi cm^3=3600\pi cm^3`

We know that the ice cream comes in cylindrical cartons, so we have to find the volume of ice cream each carton contains, if the radius is 11 cm and the height is 30 cm,

`V_(carton)=\pi\cdot r^2\cdot h=\pi\cdot11^2cm^2\cdot30cm=3630\pi cm^3`

Note that the volume of one carton of ice cream contains 30π cm³ more volume of ice cream than the volume in 100 scoops. This means that one carton will be enough to serve 100 scoops of ice cream - and there will be a little less than one scoop left.