MTH/SLS218-6816
Exam2
31, 2009
.t
NAME,
ProfessorIIya Kofman
)
rg1
1in - 2.54cm,
1kg : 2.2lbs
1 gal - 3.791
Problem 1. A right rect-angularprism is 4ft long, 2ft wide, gft deep.
(") What is the volume of the prism?
L'l #+e
(b) If a cube 6 in by 6 in by 6 in is filled with water, how many such cubes will fill
t=
zI{tsx
,;:i"i^'
l
t+t
)
W
?tf+ + /*,u
cu|L'\7'
Problem
t
fL/-'--I
6'"
I
= l??- cu{*9
2. (*) Explain the difierence between an ounce and a fluid ounce,
Qu,^t* = u^;+ t
*1. of = 11ut?
IQ-UL+ (',.att)
"?
ue&'u^t-
(b) How many m(, arc in 1 pt?
ry*
I p+x Wx
gf+e
F'-
-'? 473
ryry'^'e
u^!|
ll
(") Whichismorewater,apoundorapintof
water?Justify. tAsg fn e =t
/p+r ,#r*
trrcdII,n
#" = I73y + yiw(i, ahor'--
ItLx #-r* 'ry =15'/fl
(d) Which is more, I oz or L ff, oz of water? (1 lb - 16 oz, and 1 pt - lG fl oz)
lf'{ot- ry A
lot =ryil
e"*"\
3o
+
(/
ot is c.'.ot\-
Tf-GX
%'(fr
Problem 3. (") How many kilogramsis one million centigrams?
x
MfffirW=lo
tolca
J
1oil
(b) one acreis 43,tuo tt"#ftn;t
k7,
L a square
milein acres?
f sru^;
* W".
= 6'loo.
ffi*"= Hq*(
(") The peregrinefalconis the fastestanimal on earth, clockeddiving at 80m/sec.
How fast is that in miles per hour?
80y
94
(d) The density of lead is 11 Sl^L What is that in poundsper gallon?
rry\Tf
l{fl/^nx
,#,xry.
,-r-lr.,^
/tot,-,
{Wu^:
r_
\) _ _ ___r*'r
U^i
e (L{of-^
= ?A .,ft'/V"t
(") The distanceto Chicagois 800miles. The distanceto the moon is 380,000km.
How many trips to Chicagois one trip to the moon?
x ttfu,"
!4-^.
,
&),
*U
2.flc- I Ltn f,zto+(
t
t"
'ffi
380,W (an ..
-ffilWou\.
(tla,nnl',Ir
latlcnq
t\
fAO o'^i
l^r
3go,Y =?-?f
= L1 S lrtvrS-1"rAt>atro
l-6
K^
(LYo
produces
glaze
per
year.
(r)
A
1500
toys
If
how
company
one
cup
of
covers
toys,
5
S
Borua
many liters of glaze are needed each month?
ttgofu r lyr x I4
f 1"7s
V{
((oc^ft
K gg*y,.=5.?!./^",n
l?'wc'fts
fr4
w-
Problem 4. The diameter of a human hair is about 50 ptm. (L p* is called a
micron. Imm - 1000 microns.) If you laid hairs that are 1in long next to each
other, how many hairs would be needed to cover 1 square inch?
I ,-,:
7'I''{"^
^r
/i,n x \_-r lo'goo'a'u
(c'^
lia
q qoL
S
_ T o'h
/lt
Lf+ lo
I loo'-,
-=
,s;??voilt^
cncl
'
5O8 halvs
Problem 5. (") If the dots are spaced1 cm apart, computethe areaof the quadrilateral shown.
aooooaoooo
tl l";z^abs&tea':
q:
+ (gg)+L(z"1)4l,z"t)+tLI
oo
o
ooo
o
o
= 11 cb\u
oooooooooo
(b) What is the areaof a quadrilateralwith perpendiculardiagonalsthat are 8 cm
and 10cm long?
+(g'to)
= 40 Lu4L
Problem 6. Recall our proof of the PythagoreanTheorem. Given four copiesof
a right triangle with sidesa,b,c such that a'+b2 : c2, what is the area of the
shadedregion?
c>
Problem 7. (") A kite is flying on a 25m line, and its shadow is 7m away. If
the sun is directly overhead, how high is the kite? Justify.
W-?L
> 74w
(b) If a triangle has side lengths 8, 15,18, can it be a right triangle? Justify.
No" g'+(t-* tg'
(") What is the longest pole that can fit in a box that is 4 feet long, 3 feet wide,
and 5 feet tall? Showwork.
n 3'+s' :.1fi
5 pat <oQ
3o
= S,lLH 7,/ (t
Problem 8. (") Compute the a,reaof region A. (b) Compute area of region B.
Showwork.
hr
a.>+lq+6-',1
A
=w.sl
-1
,
10
ht
dttt'**'
{1/fh.
2
t) $+6+Lt?'
3
\
1\
1
2
3Er
6
=3O
de 4u-6'Lp
2
=9O
f r q-^ I''' \
t Y I
U
Problem g. (BONUS) Sarnreports that a plate weighs2lbs. Alice reports that
a vulseweighs 2.0lbs. Bob can weigh things in pounds to two decimal places.
(") If Alice weighsthe plate, what weight range could she report?
I' f €' 7,'l ,(Lg
(b) If Bob weighsthe vase,what weight range could he report?
l,qt - ?'0'l '(Ls
(") If Bob weighsthe plate, what weight range could he report?
l,5o
lV+t{
?.qq lLs