Sample question
Question
Calculate the length of each arc and area of each sector to 3 decimal places.
Sector 1
\(Arc\,length = \frac{{Angle}}{{360^\circ }} \times \pi d\)
\(= \frac{{72}}{{360}} \times \pi \times 10\)
\(= 6.283185...\)
\(= 6.283\,(to\,3\,d.p.)\)
\(Area\,of\,sector = \frac{{Angle}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{72}}{{360}} \times \pi \times {5^2}\)
\(= 15.70796...\)
\(= 15.708c{m^2}(to\,3\,d.p.)\)
Sector 2
\(Arc\,length = \frac{{Angle}}{{360^\circ }} \times \pi d\)
\(= \frac{{45}}{{360}} \times \pi \times 8\)
\(= 3.14159...\)
\(= 3.142\,(to\,3\,d.p.)\)
\(Area\,of\,sector = \frac{{Angle}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{45}}{{360}} \times \pi \times {4^2}\)
\(= 6.28318...\)
\(= 6.283c{m^2}(to\,3\,d.p.)\)
Sector 3
\(Arc\,length = \frac{{Angle}}{{360^\circ }} \times \pi d\)
\(= \frac{{150}}{{360}} \times \pi \times 24\)
\(= 31.4159...\)
\(= 31.416\,(to\,3\,d.p.)\)
\(Area\,of\,sector = \frac{{Angle}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{150}}{{360}} \times \pi \times {12^2}\)
\(= 188.49555...\)
\(= 188.500\,c{m^2}(to\,3\,d.p.)\)
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