Question

An oil company distributes oil in a metal can shaped like a cylinder that has an actual radius of 5.1 cm and a height of 15.1cm. A worker incorrectly measured the radius as 5 cm and the height as 15cm. determine the relative error in calculating the surface area, to the nearest thousandth.

Answer 1

do you know how to calculate the surface area of a cylinder?

Answer 2

sa= 2pir^2+ 2pi r h

Answer 3

\[2 pir^2+2pirh\]

Answer 4

ok, so now introduce a small margin of error in 'r' and 'h' - since both have the same margin of error, lets call it 'e'. then we get:\[sa=2\pi r(r+h)\]and\[sa_e=2\pi (r+e)(r+e+h+e)\]

Answer 5

if you expand this and subtract to get \(sa-sa_e\) that will give you your margin of error in terms of 'e'

Answer 6

im so confused

Answer 7

ok, which part confuses you?

Answer 8

how to find relative error

Answer 9

relative error is defined as: (error)/(original value)

Answer 10

using the symbols above, it would be:\[\frac{sa-sa_e}{sa}\]

Answer 11

i have a formula

measured - actual/ actual

Answer 12

so you could just calculate the surface area \(sa\) using r=5.1 and h=15.1. then calculate the erroneous surface area \(sa_e\) using r=5 and h=15. and then just plug these values into the formulae above.

Answer 13

yes - sorry - the relative error is as you say:\[\frac{sa_e-sa}{sa}\]

Answer 14

I got the subtraction the wrong way round when I entered it above.

Answer 15

if you use the formulae I showed above, the relative error comes out to be:\[\frac{2\pi(r+e)(r+h+2e)-2\pi r(r+h)}{2\pi r(r+h)}=\frac{(r+e)(r+h+2e)-r(r+h)}{r(r+h)}\]
r=5.1, h=15.1, e=-0.1

Answer 16

this simplifies to:\[\frac{3er+eh+2e^2}{r(r+h)}\]don't worry if you don't understand this way of doing it. you can just calculate the surface areas using the actual and measured values of r and h and then just use the formulae you had - that will also work.

Answer 17

can you do the work with my formula please

Answer 18

why don't you show me what you have calculated?

Answer 19

m-a\a =(15-5)-(15.1-5.1)\ 15.1-5.1

Answer 20

no - that is wrong
a = the actual surface area = \(2\pi r(r+h)\) with r=5.1, h=15.1
m = the measured surface area = \(2\pi r(r+h)\) with r=5, h=15

Answer 21

again confused

Answer 22

so first calculate the actual surface area 'a' - what do you get?

Answer 23

you can use wolfram alpha to help you with these types of calculations.
see here: http://www2.wolframalpha.com/input/?i=2*pi*r%28r%2Bh%29%2C+r%3D5.1%2C+h%3D15.1

Answer 24

do you understand?

Answer 25

no

Answer 26

ok, first work out the surface area of the can using the actual dimensions for r and h. do you know how to do that?

Answer 27

nooo

Answer 28

you gave the correct formule for surface area above (\(sa=2\pi r^2+2\pi rh\)). are you saying you do not know how to use this formulae to work out the surface area?

Answer 29

i didnt know i had to get surface area

Answer 30

the question you posted states "determine the relative error in calculating the surface area, to the nearest thousandth"
so you need to calculate the surface area.

Answer 31

i dont know how

Answer 32

you know the formulae for working it out - correct?

Answer 33

i dont know how todo the entire thing

Answer 34

that is why I am trying to break it down into small steps for you.
so first we need to calculate the surface area of the actual can using the formulae that you correctly gave as:
sa= 2pir^2+ 2pi r h

Answer 35

on the original can, r=5.1, h=15.1, so we get:

sa = 2 * PI * (5.1)^2 + 2 * PI * 5.1 * 15.1

you can calculate that number can't you?

Answer 36

647.29

Answer 37

they want the answer to the nearest thousandth, so you will need more decimal places, but the basic answer is correct.

ok, next step is to calculate the measured surface area by using r=5, h=15. what do you get for that?

Answer 38

647.29375

Answer 39

647.293

Answer 40

yes - that is correct for the actual surface area. now what do you get for the measured surface area?

Answer 41

I would use 647.29375 until you get to the end to avoid rounding errors

Answer 42

what do i write on my paper to gt the right anwser

Answer 43

& idk how to do that

Answer 44

first you need to calculate the measured surface area using r=5, h=15 in formulae. i.e.:

measured sa = 2 * PI * (5)^2 + 2 * PI * 5 * 15

what answer do you get for this calculation?

Answer 45

628.31853

Answer 46

correct, so now, finally, we can work out the relative error as:

relative error = (measured - actual)/actual = (628.31853-647.29375)/647.29375

what do you get for this?

Answer 47

627.318

Answer 48

that is wrong - try again

Answer 49

(628.31853-647.29375)/647.29375

Answer 50

-.029

Answer 51

thats it! well done! we finally got there - thanks for trying...

Answer 52

a lot of people just up

Answer 53

**just give up

Answer 54

thats the final anwser?

Answer 55

yes

Answer 56

lol it only took an hour

Answer 57

I hope you understood how you got there

Answer 58

kind of
you know i still have a bunch of questions in my packet

Answer 59

np - I'll try and help if I can - I need to go and eat something now.

Answer 60

please type each question separately on the list to the left.

Answer 61

that way you will get more people helping you

Answer 62

k thanks bye

Answer 63

bye