Faid arc agus farsaingeachd seactor
Farsaingeachd seactor
'S e farsaingeachd cearcaill = \(\pi {r^2}\).
'S e am foirmle airson farsaingeachd seactor cearcaill obrachadh a-mach:
\(Farsaingeachd\,seactor = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi {r^2}\)
Eisimpleir
Ceist
Obraich a-mach farsaingeachd an t-seactor san diagram.
Farsaingeachd seactor:
\(= \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{144}}{{360}} \times \pi \times {3^2}\)
\(= 11.309...\)
\(= 11.31\,cm^{2}\)
Question
Obraich a-mach faid gach arc agus farsaingeachd gach seactor gu 3 ionadan deicheach.
Seactor 1
\(Faid\,arc = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi d\)
\(= \frac{{72}}{{360}} \times \pi \times 10\)
\(= 6.283185...\)
\(= 6.283\,(gu\,3\,id)\)
\(Farsaingeachd\,seactor = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{72}}{{360}} \times \pi \times {5^2}\)
\(= 15.70796...\)
\(= 15.708\,c{m^2}(gu\,3\,id)\)
Seactor 2
\(Faid\,arc = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi d\)
\(= \frac{{45}}{{360}} \times \pi \times 8\)
\(= 3.14159...\)
\(= 3.142\,(gu\,3\,id)\)
\(Farsaingeachd\,seactor = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{45}}{{360}} \times \pi \times {4^2}\)
\(= 6.28318...\)
\(= 6.283\,c{m^2}(gu\,3\,id)\)
Seactor 3
\(Faid\,arc = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi d\)
\(= \frac{{150}}{{360}} \times \pi \times 24\)
\(= 31.4159...\)
\(= 31.416\,(gu\,3\,id)\)
\(Farsaingeachd\,seactor = \frac{{\text{Ce脿rn}}}{{360^\circ }} \times \pi {r^2}\)
\(= \frac{{150}}{{360}} \times \pi \times {12^2}\)
\(= 188.49555...\)
\(= 188.500\,c{m^2}(gu\,3\,id)\)