Question

Elena deseneaza pe hartie tiparul unei fuste din figura alaturata(o parte a unui sector de cerc).
a)Care este lungimea taliei?
b)De cat aterial are nevoie Elena pentru confectionarrea fustei?

Answer 1

$a)~ L_{1}= \frac{150 \textdegree}{360 \textdegree}*2 \pi R_{1} = \frac{5}{6}* \pi *27= \frac{45}{2} \pi ~(cm). \\ L_{2} = \frac{150 \textdegree}{360 \textdegree}*2 \pi R_{2}= \frac{5}{6}* \pi *77= \frac{385}{6} \pi ~(cm). \\ \\ L_{talie} = L_{1}+ L_{2}+2*50= \frac{45}{2} \pi + \frac{385}{6} \pi +100= \frac{260}{3} \pi +100~(cm).$

$b)~ A_{1}= \frac{150 \textdegree }{360 \textdegree} * \pi * R_{1}^2= \frac{1215}{4} \pi ~(cm^2). \\ A_{2}= \frac{150 \textdegree}{360 \textdegree}* \pi * R_{2}^2= \frac{29645}{12} \pi ~(cm^2). \\ \\ A_{mat.}= A_{2} - A_{1}= \frac{6500}{3} \pi ~(cm^2).$