Question

Jim has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 7 inches, what is the largest number of full milk glasses that he can pour from one gallon of milk? (Note: There are 231 cubic inches in 1 gallon.)

Answer 1

The first we have to know is the formula for the volume of a cylinder:

`V=\pi\cdot r^2\cdot h`

From the question, we have that

D = 3 inches --> r = 3/2 --> r = 1.5 inches

h = 7 inches

Then, we have that the volume is:

`V=\pi\cdot(1.5)^2\cdot7\Rightarrow V=49.48008\approx49.48`

Then, the cylinder (glass) has a volume of 49.48 cubic inches.

If we know that there are 231 cubic inches in a gallon, we have that:

`N=(231)/(49.48)\Rightarrow N=4.6685\approx4.67`

Then, from the result, we can say that the largest number of full milk glasses that he can pour from one gallon of milk is 4 glasses.