math 2.1
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School
Southern New Hampshire University *
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Course
142
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
4
Uploaded by GeneralIronOkapi37
The height of the cylinder is 8 inches.
We'll be analyzing the surface area of a round cylinder - in
other words the amount of material needed to "make a can".
A cylinder (round can) has a circular base and a circular top
with vertical sides in between. Let
r
be the radius of the top
of the can and let
h
be the height. The surface area of the
cylinder,
A
, is
A=2πr^2+2πrh
A=2πr^2+2πrh (it's two circles
for the top and bottom plus a rolled up rectangle for the
side).
Part a
: Assume that the height of your cylinder is
8
inches.
Consider
A
as a function of
r
, so we can write that
as
A
(
r
)=
2
πr^
2
+
16
πr A(r)=2πr^2+16πr
. What is the domain of
A
(
r
)
? In other words, for which values of
r
is
A
(
r
)
defined?
The domain is represented as any real positive number greater than 0.
0<
infinity
Part b
: Continue to assume that the height of your cylinder
is
8
8 inches. Write the radius
r
as a function of
A
. This is the
inverse function to
A(r)
, i.e to turn
A
as a function
of
r
into.
r
as a function of
A
.
On Part B I was completely confused finding the inverse of PI
it threw me for a loop. I watched several videos to see step
by step of finding the inverse by couldn’t find one to help.
(A)= 2πr
2
+16πr
(A)-A = 2πr
2
+16πr – A
0 = 2πr
2
+16πr - A
(A)
= 2πA
2
+
16πA
2π 2π 2π
(A)
= 2π
A
2
+
16π
A
2π 2π
2π (A)
= A
2
+ 8A A(A+8) 2π (A)-8 = A(A+8) -8 2π (A)-8 = A
2
2π (A)
- 8 = A
2
2π r -1
(A) = (A)
- 8 2π
Part c
: If the surface area is
275
square inches, then what is
the radius
r
? In other words, evaluate
r
(
275
)
.
Round your
answer to 2 decimal places.
SA=275 H= 8
275= 2πr
2
+(2)πr(8)
275
= 2πr
2
+
16πr
2π 2π 2π
275
= 2π
r
2
+
16π
r
2π 2π 2π
275
= r
2 + 8r
2π 275*2(3.14)
=
43.78
43.78= r
2 + 8r
The forth decimal the number to represent the radius is
3.7391 would make the radius 3.7319 the equation would
equal 43.7822, but having to round to the second decimal
3.73 would be the approximate radius.
R 3.73
R *
R
2
+
8
Total
2
2
16
20
3
9
24
33
4
16
32
48
3.5
12.25
28
40.25
3.7
5
14.06
30
44.06
3.7
4
13.98
29.92
43.90
3.7
3
13.91
29.84
43.75
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