Circles, SM-Bank 055

A plane is circumnavigating the earth at the equator. It is cruising at a constant altitude of 10 kilometres above the earths' surface.

Given the earths' radius is approximately 6400 kilometres at the equator, calculate the distance, \(d\), that the plane has travelled after completing one lap of the earth.

Give your answer correct to the nearest whole kilometre. (3 marks)

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\(40\ 275\ \text{km (nearest whole kilometre)}\)

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\(\text{Radius of planes’ path}=6400+10=6410\ \text{km}\)

\(d\)	\(=2\pi r\)
	\(=2\pi \times 6410\)
	\(=40\ 275.2178\dots\)
	\(=40\ 275\ \text{km (nearest whole kilometre)}\)

\(\therefore\ \text{The distance the plane travels around the earth}\)

\(\text{at the equator is approximately }40\ 275\ \text{kilometres.}\)