Container radius problem

Question

PS: the word pie stands for the pie in math. 3.14 etc.

 

A cylindrical container of internal radius 2 inches and internal volume 32 pie  cubic inches is 3/4 filled with water. What is the maximum number of cylindrical disks of radius 2 inches and height 3/5 inch  that can be added to the container without letting the water overflow?

Answer 1

Find the height of the cylinder using the formula for the volume:

V = π r² h

(The "pie" symbol looks more like the letter "n" that is a limitation of the font in this program.)

^{32 = π * 4 * h}

^{h = 32 /  ( π * 4 ) = 2.55 inches}

The water stops at 3/4 of the height so the water goes to the 3/4 * 2.55 = 1.91 inches level

Each disk is 3/5 inches = .6 inches thick so 1.91 / .6 = 3.18 disks can be added.

If we add 4 disks, then water will spill out so the maximum number of disks is 3.