# I need help!

• Jun 28th 2006, 09:17 AM
babygirl
I need help!
Approximately 118 mi wide and 307 mi long and averaging 279 ft in depth, Lake Michigan is the second-largest Great lake by volume. Estimate its volume of water in m3. (Note that 2.54 cm = 1 inch and 5280 feet = 1 mile)
• Jun 28th 2006, 10:39 AM
Soroban
Hello, babygirl!

This involves converting units . . . can you do that?

Quote:

Approximately 118 mi wide and 307 mi long and averaging 279 ft in depth,
Lake Michigan is the second-largest Great lake by volume.
Estimate its volume of water in m³.
(Note that 2.54 cm = 1 inch and 5280 feet = 1 mile)

Volume is Length x Width x Height (Depth).

So we have: .$\displaystyle V \;= \; 118\text{ miles} \times 307\text{ miles} \times 279\text{ feet}$

Converting miles to meters and feet to meters, we have:
. . $\displaystyle V\;=\;189,902.59 \times 494,068.61 \times 85.04 \;=\;7.9778870234 \times 10^{12}$ m³.

The volume of Lake Michigan is about $\displaystyle 8 \times 10^{12}$ (eight trillion) cubic meters.

• Jun 28th 2006, 11:07 AM
Ruler of Hell
Just asking, where'd that 10¹² come from? Meaning like the answer is 7978870233866.559496 so where'd you get the 10¹² from? shouldn't it be 10 razed to 6? Sorry but I'm confused.. I'm a Math rookie...

Btw, what are the values for converting Miles to Metres?
• Jun 28th 2006, 11:45 AM
CaptainBlack
Quote:

Originally Posted by Soroban
Hello, babygirl!

This involves converting units . . . can you do that?

Volume is Length x Width x Height (Depth).

So we have: .$\displaystyle V \;= \; 118\text{ miles} \times 307\text{ miles} \times 279\text{ feet}$

Converting miles to meters and feet to meters, we have:
. . $\displaystyle V\;=\;189,902.59 \times 494,068.61 \times 85.04 \;=\;7.9778870234 \times 10^{12}$ m³.

The volume of Lake Michigan is about $\displaystyle 8 \times 10^{12}$ (eight trillion) cubic meters.

I would have thought a better approximation would treat the lake as an ellipse
rather than a rectangle. This would result in an area $\displaystyle \pi/4$ times that of the
corresponding rectangle, and as we are given an average depth rather than
maximum depth the volumes would scale by the same factor. This would
reduce the estimated volume to $\displaystyle \approx 6 \times 10^{12}\ m^3$.

RonL

By the way the claimed volume is $\displaystyle \approx 4.9 \times 10^{12}\ m^3$
• Jun 28th 2006, 11:54 AM
earboth
Quote:

Originally Posted by Ruler of Hell
...
Btw, what are the values for converting Miles to Metres?

Hello,

have a look here: http://en.wikipedia.org/wiki/Conversion_factor

1 mile = 1609.344 metres

Greetings

EB