   Chapter 15, Problem 37RE

Chapter
Section
Textbook Problem

Find the volume of the given solid.37. The solid tetrahedron with vertices (0, 0, 0), (0, 0, 1), (0, 2, 0), and (2, 2, 0)

To determine

To find: The volume of the given solid.

Explanation

Given:

The region E is the tetrahedron with vertices (0,0,0),(0,0,1),(0,2,0),(2,2,0) .

Formula used:

The volume of the given solid is given by, V=EdV .

Calculation:

From the given conditions, it is observed that the equations of the planes which is the sides of the tetrahedron are y=2,x=y and y+2z=2 . Then, the volume of the given solid is,

V=EdV=020y02y2dzdxdy

Integrate with respect to z and apply the limit.

V=020y[z]02y2dxdy=020y[2y20]dxdy=020y(1y2)dxdy

Integrate with respect to y and apply the limit

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