Geometry word problem?

Question

3.A drug manufacturing company wants to manufacture a capsule that contains a spherical pill inside. The diameter of the pill is 4mm and the capsule is cylindrical, with hemispheres on either end. The length of the capsule between the two hemispheres is 10mm. Describe how we could find the exact volume the capsule will hold, excluding the volume of the pill

How do I find the radius and height?

Answer 1

About 125 mm^3.

First decompose the capsule. It has the two hemispheres and, removed and joined, they form a sphere of the same size as the pill (assuming as I will that the pill just touches the sides of the cylinderical portion). Then we have remaining a standard cylinder. Since you need the volume of the capsule minus the volume taken up by the pill, set the two hemispheres aside with the pill and figure the cylindrical part's volume:

Volume of cylinder = pi * radius^2 * height

so: volume = pi * (½ * 4 mm)^2 * 10 mm = 40 * pi mm^3 = 125.6 mm^3

Answer 2

I assume the spherical pill inside is the largest one that would fit inside the capsule.

Think of cutting the spherical pill into two pieces, put one-half in each hemisphere at the end of the cylinder. Then the volume that remains is that of a cylinder with flat ends. The volume of a cylinder with flat ends is:

πr²h = π(4/2)²(10) = 40π mm³

This is the volume of the cylinder desribed in the problem exluding the spherical pill.

Answer 3

You would have to find the volume of the cylinder, which is height*pi*r^2, which would be 40pi.
Then, add the volume of the two hemispheres, which is pi*r^2 or 4pi.
So the answer is 44pi.
There.

Answer 4

water displacement?

Answer 5

uuuuuuuuuuh... what?