Dimension Analysis Word Problem

[geekily]

Suppose that evrey week, the average American eats 1/4 pizza. The average pizza has a diameter of 14 inches. The are about 250,000,000 Americans, and there are 640 acres in a square mile. About how many acres of pizza do Americans eat every week?

I set this up as (250,000,000 Americans) (.25 pizza/1 Amer) (14 in/1 pizza) (1 ft/12 in) (1 mi/5280 ft) (1 mi/5280 ft) (640 acres)

I also tried substituting both the area of the pizza and the circumference of the pizza for 14 inches, and I also tried multiplying everything except the 250 mil Americans twice instead of just the 1/5280 ft to get to square miles, and also everything except the the 250 mil Americans and the .25 pizza. Nothing gets me to the right answer, which is 1534 acres. What am I doing wrong?

Thanks for your help!

 

[Deleted member 4993]

Suppose that evrey week, the average American eats 1/4 pizza. The average pizza has a diameter of 14 inches. The are about 250,000,000 Americans, and there are 640 acres in a square mile. About how many acres of pizza do Americans eat every week?

I set this up as (250,000,000 Americans) (.25 pizza/1 Amer) (14 in/1 pizza) (1 ft/12 in) (1 mi/5280 ft) (1 mi/5280 ft) (640 acres)

I also tried substituting both the area of the pizza and the circumference of the pizza for 14 inches, and I also tried multiplying everything except the 250 mil Americans twice instead of just the 1/5280 ft to get to square miles, and also everything except the the 250 mil Americans and the .25 pizza. Nothing gets me to the right answer, which is 1534 acres. What am I doing wrong?

Thanks for your help!

Area of one pizza = pi/4 *14^2 sq.in = pi*49 sq.in = ~154 sq.in

Remember you are dealing with area - not just length.

 

[stapel]

Since you're working with area ("acres"), you probably want to use the area of the pizza (based on the radius), not the length of the diameter of the pizza, and convert square (area) units, not linear (length) units. :wink:

Eliz.

 

[TchrWill]

Suppose that evrey week, the average American eats 1/4 pizza. The average pizza has a diameter of 14 inches. The are about 250,000,000 Americans, and there are 640 acres in a square mile. About how many acres of pizza do Americans eat every week?

I set this up as (250,000,000 Americans) (.25 pizza/1 Amer) (14 in/1 pizza) (1 ft/12 in) (1 mi/5280 ft) (1 mi/5280 ft) (640 acres)

I also tried substituting both the area of the pizza and the circumference of the pizza for 14 inches, and I also tried multiplying everything except the 250 mil Americans twice instead of just the 1/5280 ft to get to square miles, and also everything except the the 250 mil Americans and the .25 pizza. Nothing gets me to the right answer, which is 1534 acres. What am I doing wrong?

Thanks for your help!

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Pizza area = Pi(14^2)/4 = 154 in.^2

Each American eats 1.4 pizza per week, or 38.5 in.^2 per week.

Pizzas eaten by 250,000,000 Americans per week is therefore 38.5(250,000,000) = 9,625,000,000 in.^2 per week.

9,625,000,000 in.^2/week x (1 sq.ft./144 sq.in.) = 66,840,277.78 ft.^2/week

666,840,277.78 sq.ft./week x 1 acre/43,560 sq.ft. =
1534.44 acres/week.

Yummy!!

 

[geekily]

Great! Thank you both. Stapel, like you suggested, using square units made my formula work. I'm still not sure why my teacher told us it's easier to multiply everything twice rather than just square it right off the bat, but I tried it again that way, multiplying everything but the 250 mil Americans and .25 pizza twice, and it did work out - maybe it's just a matter of learning what I do and don't need to square. But anyway - thank you very much! Problem solved.