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For the part circled in red, I don't understand how we knew to set these up . Where did s/2/a/2 come from? Which equation are we using to find this.? Is it something for area? Same for h-y/h   how did we know to set it up like this

For the part circled in red, I don't understand how we knew to set these up . Where did s/2/a/2 come from? Which equation are we using to find this.? Is it something for area? Same for h-y/h   how did we know to set it up like this

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 38E: Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 6,...
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For the part circled in red, I don't understand how we knew to set these up . Where did s/2/a/2 come from? Which equation are we using to find this.? Is it something for area? Same for h-y/h   how did we know to set it up like this. 

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 a h-y → S-n (n-4) 2 %3D -> T-axis Thereforo the ava Aly) of the cross (a) 15. section at 4 I5 a B, ACy) =5²= V= S ACy) dy S he (n-y)a h-y 11 131 volume is んマ ん (h-y)°dy a ha(h-y)?d (b)
Transcribed Image Text: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 a h-y → S-n (n-4) 2 %3D -> T-axis Thereforo the ava Aly) of the cross (a) 15. section at 4 I5 a B, ACy) =5²= V= S ACy) dy S he (n-y)a h-y 11 131 volume is んマ ん (h-y)°dy a ha(h-y)?d (b)
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