A cylindrical cooler

Question

A cylindrical cooler had a diameter of 30 inches and a height of 24 inches. Runners in a marathon can use cone shaped cups to get a drink from the cooler. I'd the cops have a radius of 3 inches and a height of 4 inches, how many full cups would be able to be filled from the cooler?

Answer 1

Volume of the cylindrical cooler is found by the formula:  V_cyl=πr²h
Volume of the cone-shaped cup is found by the formula:  V_cup=(1/3)Πr²h

 

Volume of our cylinderical cooler is (pi)(15)²(24) = 5400π

 

Volume of 1 cup = (1/3)(pi)(3)²(4) = 12π

 

So now we just need to find out how many "12π"s can fit into 5400π.

 

This is a division problem:   5400π/12π  =  450

 

So 450 full cups would be able to be filled from the cooler.