A map of Nelson County is laid out in the standard (x,y) coordinate plane below, where the center of the county is at (0,0). a cell phone tower is at (5,4) and Esteban's house is at (10,-2). each coordinate unit represents 1 mile. the tower signal range is 10 miles in all directions. how much land area to the nearest 10 miles does the tower signal range cover? a=80^2 b=100^2 c=310^2 d=400^2

Question

19-10-2014
Mathematics

Answered

A map of Nelson County is laid out in the standard (x,y) coordinate plane below, where the center of the county is at (0,0). a cell phone tower is at (5,4) and Esteban's house is at (10,-2). each coordinate unit represents 1 mile. the tower signal range is 10 miles in all directions. how much land area to the nearest 10 miles does the tower signal range cover? a=80^2 b=100^2 c=310^2 d=400^2

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AL2006 AL2006 · Answer 1 · 2014-10-19T17:23:35-04:00

Wow ! They're really trying hard to confuse you with this one.

You don't need to know anything about Nelson County, its grid layout, Esteban's house, or the location of the cell tower. All of that is just
chaff and sprinkles.

All you need to know is: The tower covers everything within 10 miles of it.
So the coverage area is a circle, with radius = 10 miles and the tower in
the center.

The area of the circle is (pi) (radius-squared) = 100 (pi) = 314 square miles.