Math Is Fun Forum

justin115

Guest

Ratio

I have a problem that has been bugging me.

An air traffic control radar screen is a circle with a diameter of 24 inches. What is the area of the screen to the nearest square inch.

answer is 452 in^2

The second part of the question says there is a scale so that 6 inches: 25 nautical miles.
What is the area of the circular region covered by the radar.

So I did it two different ways and got the same answer. I figured out that for every 1 inch you have 4.1 nautical miles and then multiplied that by 452 for a total of 1853 nautical miles.

I also divided 452 into groups of 6, found there were 75.33 and again got 1853.

Unless I am misunderstanding the concept of ratios I believe this should be the answer. However, the answer book is telling me it should be

7850

is this a misprint?  Or am I just not seeing something.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Ratio

You're given a scale for length, but you're trying to convert an area.
You can get an appropriate scale by squaring everything, to get 36 in² : 625 mile²

Alternatively, put the screen's diameter of 24in into the original scale to find the diameter of the range in miles, and work out the range area from that.

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Why did the vector cross the road?
It wanted to be normal.

Justin115

Guest

Re: Ratio

Ahh. Wasn't reading closely enough. Thank you.