# Find the volume of the solid with cross-sectional area...

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Name: Sandro M. Cruz College ID: 0543718 Thomas Edison State College Calculus II (MAT-232) Section no.: OL010 Semester and year: Oct 2015 Term Written Assignment 1 Answer all assigned exercises, and show all work. Each exercise is worth 5 points. Section 5.2 2. Find the volume of the solid with cross-sectional area A ( x ). 0 e
6. Find the volume of a pyramid of height 160 feet that has a square base of side 300 feet. These dimensions are half those of the pyramid in example 2.1. How does the volume compare?
We have f(x) = - 15 8 x + 300 The cross sectional is the square of f(x): V = 0 160 A ( x ) dx V = 0 160 ( 15 8 x + 300 ) 2 dx =====> u = ( 15 8 x + 300 ) , du = 15 8 dx V = 8 15 0 160 u 2 du = 8 45 ( 15 8 x + 300 ) 3 | 160 0 V = [ 8 45 ( 300 15 8 ( 160 )) 3 ] – [ 8 45 ( 300 15 8 ( 0 )) 3 ] = 0 – (- 4800000) V = 4800000 ft 3 Even though the dimensions of the pyramid in this exercise are half of those from example 2.1, the volume for this pyramid of height 160 and square side of 300 is not even half of the volume of the one with the original dimensions. There is a difference of 33600000 ft 3 . 10. A dome “twice as big” as that of exercise 9 (see text) has outline 2 120 120 x y for 120 120 x (units of feet). Find its volume. )
WA 1, p. 2
The volume is: V = 0 120 π . ( 120 ( 120 y )) 2 dy = 0 120 π . ( 120 ( 120 y )) dy V = π 0 120 ( 14400 120 y ) dy = π [ 14400 y 60 y 2 ] 120 0 = 864000. π V = 2714336 ft 3