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Unformatted text preview: ANSWER Name: K EY MA 1022  2008 B Term Section A02
November 25, 2008 Quiz — Sections 6.3, 6.5, 6.6 1. Let R be the region below the line y = x — 3 , above the x H axis , and to the left of x = 5 . Using the method of cylindrical shells, SET UP
BUT DO NOT EVALUATE an integral to determine the volume of the solid generated by rotating the region R around they  axis. (12 points) 2. BONUS QUESTION You are running a marathon, and you pass the
second place runner. What place are you in now? (2 points) SECOND PLAcE 3. Let R be the region to the right of the y — axis , bounded by the equations: y = x3 and y = 2 — x2. Using the method of cylindrical
shells, SET UP BUT DO NOT EVALUATE an integral to determine
the volume of the solid generated by rotating the region R around the
line x = 5 . (12 points) X3: ZX"
Xe I
II
: l 111 (s’xX 1X‘X’) 4*
0 4. BONUS QUESTION You are running in a marathon with eight other
runners, and you pass the last place runner. What place are you in now? (2 points) [vbr (705513 LE — IF YOU ARE BENIN!)
1H6 M57 Ponce Runner.) [gu'o 66'
m MST pm (6 YOURSQF.’ 5. SET UP BUT DO NOT EVALUATE an integral to determine how
much work is needed to empty a conical tank full of water which is
sitting on the ground, point down (like an ice cream cone), if all of the
water is to be liﬁed to a point 20 feet above the ground. The cone has
height of 8 feet and radius of 3 feet. Assume the density of water is equal to p. (10 points) 6. A spring has a natural length of 10 meters. A force of 8 newtons is
required to hold it stretched out to 12 meters. How much work is done is compressing this spring from its natural length to a length of 9 meters?
(12 points) hamml length: (a
slvehhul '= 12 Conupturn»! = 7 7. Find the centroid ofthe region bounded by: y = 1+ 3x, y = x, x =1,
and x = 3 . (12points) 8. Set up but do not evaluate expression(s) to ﬁnd the centroid of the
region bounded by y = 9 — x2 and y = x — 3 . (IOpoints) ***END OF QUIZ ***** BONUS QUESTION I Visited a store at the mall last week that only sells
socks for men. The store’s Sign is shown below. I determined the centroid
of every letter on the sign, and found that the centroid of one of the letters
has a unique property. Which letter is it, and what is the unique property? Z S©X The ceml'voiol a; ”I? letter 00” I:
na’r on “‘9 letter {itself (m: Ema?
W open kale in “A: Mt'aldlc 3}. a.”
at 1“ bfker lettersl cuboid; ”e on it}; lejgx. ...
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 Spring '09
 Abraham
 Calculus

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