Derive the formula for the volume of a right pyramid whose altitude is h and whose base is a square with sides of length a.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do we set up integrals for Ex. 1.

Let S be a solid bounded by two parallel planes perpendicular to the y- axis at y= c and
y=d. If, for each y in c, d, the cross-sectional area of S perpendicular to the y-axis is
d
A(y), then the volume of the solid is V = A(y) dy provided A(y) is integrable.
Ex. 1
Derive the formula for the volume of a right pyramid whose altitude is h and whose
base is a square with sides of length a.
A-axis
B(0, h)s
T-axis
a.0)
(a)
B,
h-y
J'
(b)
Transcribed Image Text:Let S be a solid bounded by two parallel planes perpendicular to the y- axis at y= c and y=d. If, for each y in c, d, the cross-sectional area of S perpendicular to the y-axis is d A(y), then the volume of the solid is V = A(y) dy provided A(y) is integrable. Ex. 1 Derive the formula for the volume of a right pyramid whose altitude is h and whose base is a square with sides of length a. A-axis B(0, h)s T-axis a.0) (a) B, h-y J' (b)
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