EXAMPLE 8 Find the volume of a pyramid whose base is a square with side L and whose height is h. SOLUTION We place the origin O at the vertex of the pyramid and the x-axis along its central axis as in the figure. Any plane P, that passes through x and is perpendicular to the x-axis intersects the pyramid in square with side of length s. We can express s in terms of x by using similar triangles. s/2 and so s = Video Example ) Tutorial [Another method is to observe that the line OP has slope L/(2h) and so its equation is y = Online Textbook Lx/(2h).] Thus the cross-sectional area is A(x) = s' = The pyramid lies between x = 0 and x = , so its volume is L? A (2) dr = V = %3= h?
EXAMPLE 8 Find the volume of a pyramid whose base is a square with side L and whose height is h. SOLUTION We place the origin O at the vertex of the pyramid and the x-axis along its central axis as in the figure. Any plane P, that passes through x and is perpendicular to the x-axis intersects the pyramid in square with side of length s. We can express s in terms of x by using similar triangles. s/2 and so s = Video Example ) Tutorial [Another method is to observe that the line OP has slope L/(2h) and so its equation is y = Online Textbook Lx/(2h).] Thus the cross-sectional area is A(x) = s' = The pyramid lies between x = 0 and x = , so its volume is L? A (2) dr = V = %3= h?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
Related questions
Question
![EXAMPLE 8
Find the volume of a pyramid whose base is a square with side L and whose height is h.
SOLUTION
We place the origin O at the vertex of the pyramid and the x-axis along its central axis as in the
figure. Any plane Px that passes through x and is perpendicular to the x-axis intersects the pyramid in a square
h
with side of length s. We can express s in terms of x by using similar triangles.
s/2
h
L/2
L
and so s =
Video Example
Tutorial
. [Another method is to observe that the line OP has slope L/(2h) and so its equation is y =
Online Textbook
Lx/(2h).] Thus the cross-sectional area is
A(x) = s² :
The pyramid lies between x = 0 and x =
so its volume is
h
ch
L2
V:
A (x) dr
16
=
h2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fb12c12-7b1b-44b9-b21d-fe29c223440f%2F94f2fc4c-53f6-4f05-9064-91793090e2ea%2Fvd2svuf_processed.png&w=3840&q=75)
Transcribed Image Text:EXAMPLE 8
Find the volume of a pyramid whose base is a square with side L and whose height is h.
SOLUTION
We place the origin O at the vertex of the pyramid and the x-axis along its central axis as in the
figure. Any plane Px that passes through x and is perpendicular to the x-axis intersects the pyramid in a square
h
with side of length s. We can express s in terms of x by using similar triangles.
s/2
h
L/2
L
and so s =
Video Example
Tutorial
. [Another method is to observe that the line OP has slope L/(2h) and so its equation is y =
Online Textbook
Lx/(2h).] Thus the cross-sectional area is
A(x) = s² :
The pyramid lies between x = 0 and x =
so its volume is
h
ch
L2
V:
A (x) dr
16
=
h2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage