Chapter 9.CR, Problem 27CR

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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:

Volume of Half Sphere:

Volume of Sphere:

**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

The radius of the of the spherical pill is,

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

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

The radius of the cylinder and hemisphere is

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

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