?$解：\text{(1)}設(shè)圓錐側(cè)面展開圖的圓心角為n°$?
?$依題意得，\frac{n\pi ×40}{180}=2\pi ×10$?
?$解得\text{，}n=90$?
?$∴圓錐側(cè)面展開圖的圓心角為90°，$?
?$側(cè)面積=\pi ×10×40=400\pi \text{(\,\,cm}^2\text{)}$?
?$\left( 2 \right) 如圖所示\text{，}$?
?$由圓錐的側(cè)面展開圖可見，從點(diǎn)A爬到點(diǎn)B的最短路程為線段AB的長(zhǎng)度.$?
?$在Rt△ABS中，∵AS=A'S=40\,\,\text{cm}，B為A'S的中點(diǎn)$?
?$∴BS=\frac{1}{2}A'S=20\,\,\text{cm}$?
?$∴AB=\sqrt{40^2+20^2}=20\sqrt{5}\,\,\text{cm}$?
?$∴它所走的最短路程為20\sqrt{5}\,\,\text{cm}.$?
