Question

The thickness of a kerosene spill is 1.2mm. The spill is .79 miles in diameter. Kerosene has a density of .82g/cc. Assuming that the spill is uniform in thickness and is shaped in a circle, how much kerosene, volume and mass, is spilled?

Answer 1

@phi

Answer 2

I have to find the mass in tons and the volume in gallons. I have a few numbers but I messed up on the conversions

Answer 3

For example, to find the volume of the shape I used the formula of \[v = \pi r^2 h\]

Answer 4

And did half of .79 do get the r (radius)

Answer 5

I think I would work in metric
to get the volume and mass
then convert

Answer 6

Ok, is the process I did to find the volume correct though? Or should I use another formula?

Answer 7

Because I know that once I have the volume I can use that and the density to find the mass, and then carry on to my conversions

Answer 8

yes, that is the correct formula
the hard part is keeping the units consistent.

I would work with cm and g , and write the numbers in scientific notation

Answer 9

Yeah, that's what I did. I converted the 1.2 mm into .12 cm

Answer 10

But how would I do the .79 miles? Would I convert the diameter into cm or the radius?

Answer 11

google 1 mile in meters
you get
1609.344 meters
in cm that is
160934.4 cm per mile

that is one mile. the radius is 0.5*0.79 miles
if we write cm per miles as a fraction cm/mile
we want the miles to cancel, so the right thing to do is
\[ 0.5 \cdot 0.79\ \cancel{mile} \cdot \frac{160934.4 \ cm}{1 \cancel{mile} } \]

Answer 12

Um ok... where did you get the .5 from?

Answer 13

Oh never mind, that's just 1/2 right?

Answer 14

½ of the diameter

Answer 15

Yeah.. Okay let me work on it really fast

Answer 16

Ok, I got 63569.088

Answer 17

or about 6.3569e4 cm

Answer 18

I just did .5 x .79 = .395

and then .395 x 160934.4 = 6.35

Answer 19

What is the little e?

Answer 20

that is how I write 6.3569 * 10^4
the little "e" is a reminder that the next number is the exponent of (an understood) 10

Answer 21

I assume you know that 63569 can be written as 6.3569 * 10^4
?
or using my notation 6.3569e4

now find the volume
v= pi r^2 h
= 3.14* (6.3569e4)^2 * 0.12 cm^3

Answer 22

you don't type the e into the calculator , It's only to make typing easier for me.

Answer 23

or type into google
3.14* (63569)^2 * 0.12 =

Answer 24

the volume in cm^3 is
1.2492 * 10^9 cm^3

now multiply by 0.82 g/cm^3
\[ 1.2492 \cdot 10^9 \ \cancel{ cm^3} \cdot0.82 \frac{g}{ \cancel{ cm^3}} \]

Answer 25

Oh Ok! Sorry I was eating dinner

Answer 26

And then do I have to mke any other conversions?

Answer 27

Once I find the mass? I know it has to be in tons and the volume in gallons