   Chapter 9.CR, Problem 27CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

A drug manufacturing company wants to manufacture a capsule that contains a spherical pill inside. The diameter of the pill measures 4 mm. and the capsule is cylinder with hemispheres on either end. The length of capsule between the two hemispheres is 10mm. What is the exact volume that the capsule will hold? Excluding the volume of the pill?

To determine

To find:

The exact volume that the capsule will hold, excluding the volume of the pill.

Explanation

Formula used:

Volume of cylinder:

V=πr2h

Volume of Half Sphere:

V=23πr3

Volume of Sphere:

V=43πr3

Given:

A drug manufacturing company wants to manufacture a capsule that contains a spherical pill inside. The diameter of the pill measures 4 mm. and the capsule is cylinder with hemispheres on either end. The length of capsule between the two hemispheres is 10 mm.

Calculation:

Let us consider the capsule that contains a spherical pill inside as shown in the figure,

The diameter of the spherical pill is d=4 mm.

The radius of the of the spherical pill is,

r=d2=42=2 mm.

And the capsule is cylinder with hemispheres on either end. The length of capsule between the two hemispheres is 10 mm.

The height of the cylinder is h=10 mm.

Also, the radius of spherical pill is equal to the radius of the cylinder and hemispheres.

The radius of the cylinder and hemisphere is r=2 mm.

Therefore, the exact volume of the capsule and excluding the volume of the pill is,

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