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Unformatted text preview: Name: MA 1022  2007 B Term Section A02
November 20, 2007 Quiz — Sections 6.3, 6.5, 6.6 1. Using the method of cylindrical shells, calculate the volume of the solid generated by rotating around the yaxis the region bounded by: y = x2 ,
y = 8 — x2 and the y  axis. (12p0ints) b S Z‘nrhdx
6‘ 2 '2.
V: l 1Trx(8—2x‘)olx= 7m (CBXiﬁplx
0 K52
\I a“: 2'“ [dual:53] 7 X150 vz—m (IL 2)— (003] .—. 2. Using the method of cylindrical shells, calculate the volume of the solid
generated by rotating around the line it = —2 the region bounded by y=~~x2 —l , x=1, x23 andthe x—axis. (I2p0ints) 3 ‘3
V: {0.1T (x+9.)(x‘+) clx .= ’1'“ SOP' 74‘4—111) alx
\ l 3. Calculate how much work is done by the force F (y) = 53/2 pounds
in moving a particle along the y — axis from y = 1 foot to y = 3 feet.
Units matter! (10 points) Work =— ¥arce x dts'l'znce 4. A spring has a natural length of 2 meters. A force of 10 newtons is
required to hold it stretched out to 4 meters. How much work is done is
compressing this Spring from its natural length to a length of 1.5 meters?
Units matter! (12 points) AT REST "The what [enSik a?
the spring ‘us 2 meters l
l
i
i
5
a F—‘V Noh'ce I Movasl “flu Spmaj
'I’b make it easier “h; se+ E
l 7 U? My Integral ﬁn“ 042; 0.5' l
Wake:— anl o$ i
0.;
w = gm)“ : SCXAX
D 0K ' ‘ 1 l W” 8X 5 E!
2— El 0 i; ii il l 5. A cylindrical insulated tank of icy cold water is to be placed on top of the
Great Pyramid of Giza, so that thirsty visitors can have a refreshing break
after climbing to the top. ' The interior diameter of the tank will be 12 ' _
feet, and it will be 15 feet tall. The pyramid itself is 480 feet tall. The
empty tank weighs 500 pounds, and the ice water has a density of 62
pounds per cubic foot. Give an expression for the total work involved in
moving the tank plus water to the top of the pyramid. You do not have to evaluate your answer — OK to leave it as an expression. You may wish to
have two parts to your expression — one for the work moving the empty
tank, and another for the work of moving the water itself. (12 points) Work '2 ‘Pbrce X oils “have W‘; Work WOVij ewpiy {Zak
WI: 500%: x $80 FF W‘ ":— (§00)('l8‘0) "Pbol‘ PCBincl; 6. Find the centroid of the region bounded by: y = 2 + 3x, y = x ,
3C =1, and x = 3.(12p0ints) 7. Set up but do not evaluate an expression to ﬁnd the centroid of the
region bounded by y = 9 — x2 and y = 3 —~ x. (10 points) 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? 2 s @x— Th2 cewhm'ial oi enck leiler occurs
at Hae "Middle ” horizenblly Mal
VefﬁCOLHS (give—A “HAG syMMC‘I‘Yl‘QS lnvuLJ‘EQ'}; 43w ‘HLQ letter "O", Hue (Zambia!
does no} lie on ﬁve letfir ElseIC ...
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 Spring '09
 Abraham
 Calculus

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