   Chapter 10.1, Problem 42E 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

Find the volume of the solid formed when the triangular region having vertices at 2, 0 , 4, 0 , and 2, 4 is rotated about the y -axis. To determine

To show:

The volume of solid when the triangular region having vertices 2, 0, 4, 0 and 2, 4 is rotated about the y-axis.

Explanation

A triangle is drawn with the following vertices 2, 0, 4, 0 and 2, 4.

Now, the triangle is rotated about the y-axis.

The resultant will be a cone.

Now, we have to find the volume of the cone.

Let h be the height of the cone.

Let r be the radius of the cone.

From the diagram,

Height is the distance between the points 2, 4 and 2, 0.

x1,y1=2, 4

x2,y2=2, 0

Formula for distance between two points

d=x2-x12+y2-y12

Substituting the x and y co-ordinates

d=2-22+0-42

On solving this,

d=02+-42

d=42

d=16

d=4

Hence, height is 4 units.

Radius is the distance between the points 2, 0 and 4, 0

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