Andrea is preparing an installation manual for a cell-phone tower to be used in a European country. The tower specifications are in imperial units, and she must convert them to SI for their client. The specifications state that the signal for the cell-phone tower covers a circular area of radius 2.5 mi. What is this area in SI units ?
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The question is ambiguous. Do we want the radius of the region, say in kilometres, or do we want the area of the region, in say km$^2$? A mile is $1.609344$ km. So we have a circular area of radius $(2.5)(1.609344)$ km. The calculator gives radius $4.02336$ km. Such precision is absurd, $4$ km is a reasonable answer. The area of a circle of radius $r$ is $\pi r^2$. So the area of our region, in km$^2$, is $\pi((2.5)(1.609344))^2$. |
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