Dimensional Analysis of a lens

[metalmagik]

Hello everybody, I am taking a basic undergrad General Chemistry I course and am just having a little trouble brushing myself up on dimensional analysis (or factor label). This is the problem.

The area of a telescope lens is 7903 mm². (a) What is the area in square feet? (b) If it takes a technician 45 sec to polish 135 mm², how long does it take her to polish the entire lens?

I am just not so sure how to get from millimeters squared to square feet. If anyone can help me out I'd really appreciate it. Thank you.

 

[symbolipoint]

Part (a) --- Note carefully, you have millimeters*millimeters, and you want to convert to feet*feet.
1000 millimeters = 1 meter
1 meter = 100 centimeters
2.54 inches = 1 centimeter
12 inches = 1 foot.

 

[metalmagik]

Oh I see, so do I simply treat it as 1000 millimeters * 1000 millimeters and so on with the conversions?

 

[symbolipoint]

Each units equivalence relation is used as a ratio in your conversion calculation. You do not start with 1000 mm * 1000 mm [excuse the abbreviations], but you are starting with 7903 mm*mm [or in lengthy expressiveness, 7903 * millimeters*millimeters]. Use the unit equivalency relationships from there.