体积1立方米的球的表面积
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\u4e09\u89d2\u5f62=shx2 \u4e09\u89d2\u4f53=shx2\u4e58\u5bbd \u957f\u65b9\u5f62=ab \u957f\u65b9\u4f53=abh \u6b63\u65b9\u5f62=a2 \u6b63\u65b9\u4f53=a2 \u68af\u5f62=(a+b)hx2 \u68af\u4f53=(a+b)hx2\u4e58\u5bbd \u5706=3.14\uff08r\u7684\u5e73\u65b9) \u8fd8\u6709\u5706\u67f1\u4f53\u548c\u5706\u9525\uff0c\u5706\u67f1\u4f53\u662fr²\u00d7\u03c0\u00d7h\uff0c\u5706\u9525\u662f\u4e0e\u4ed6\u7b49\u5e95\u7b49\u9ad8\u7684\u5706\u67f1\u7684\u4e00\u534a\u4e09\u89d2\u4f53\u662f \u5e95\u9762\u79ef\u00d7\u9ad8\u7684\u4e09\u5206\u4e4b\u4e00 \u5706\u67f1\u8868\u9762\u79ef:2*\u03c0*\u5e95\u9762\u5706\u534a\u5f84\u7684\u5e73\u65b9+\u5e95\u9762\u5706\u5468\u957f*\u9ad8 \u4f53\u79ef:\u03c0*\u5e95\u9762\u5706\u534a\u5f84\u7684\u5e73\u65b9*\u9ad8\u5706\u9525\u8868\u9762\u79ef:\u03c0*\u5e95\u9762\u5706\u534a\u5f84\u7684\u5e73\u65b9+\u5e95\u9762\u5706\u5468\u957f*\u6bcd\u7ebf\u957f \u4f53\u79ef:(1/3)*\u03c0*\u5e95\u9762\u5706\u534a\u5f84\u7684\u5e73\u65b9*\u9ad8\u5706\u7403\u8868\u9762\u79ef:4*\u03c0*\u7403\u534a\u5f84\u7684\u5e73\u65b9 \u4f53\u79ef:(4/3)*\u03c0*\u7403\u534a\u5f84\u76843\u6b21\u65b9\u5f13\u5f62 l\uff0d\u5f27\u957f S\uff1dr2/2\u00b7(\u03c0\u03b1/180-sin\u03b1) b\uff0d\u5f26\u957f \uff1dr2arccos[(r-h)/r] - (r-h)(2rh-h2)1/2 h\uff0d\u77e2\u9ad8 \uff1d\u03c0\u03b1r2/360 - b/2\u00b7[r2-(b/2)2]1/2 r\uff0d\u534a\u5f84 \uff1dr(l-b)/2 + bh/2 \u03b1\uff0d\u5706\u5fc3\u89d2\u7684\u5ea6\u6570 \u22482bh/3 \u5706\u73af R\uff0d\u5916\u5706\u534a\u5f84 S\uff1d\u03c0(R2-r2) r\uff0d\u5185\u5706\u534a\u5f84 \uff1d\u03c0(D2-d2)/4 D\uff0d\u5916\u5706\u76f4\u5f84 d\uff0d\u5185\u5706\u76f4\u5f84 \u692d\u5706 D\uff0d\u957f\u8f74 S\uff1d\u03c0Dd/4 d\uff0d\u77ed\u8f74
解：设球的半径为R，则4/3*πR³=1 所以R³=3/4π R=三次根号3/4π
球的表面积S=4πR²=4π（三次根号3/4π）² =（6π²的2/3次方）/π
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绛旓細S=1/2*(a+L)*2蟺R锛1/2*L*2蟺r + 蟺r^2+ 蟺R^2 鐞冧綋琛ㄩ潰绉 S=4蟺R^2 浣撶Н锛屽嚑浣曞涓撲笟鏈锛屾槸鐗╀欢鍗犳湁澶氬皯绌洪棿鐨勯噺銆浣撶Н鐨鍥介檯鍗曚綅鍒舵槸绔嬫柟绫銆備竴浠跺浐浣撶墿浠剁殑浣撶Н鏄竴涓暟鍊肩敤浠ュ舰瀹硅鐗╀欢鍦ㄤ笁缁寸┖闂存墍鍗犳湁鐨勭┖闂淬備竴缁寸┖闂寸墿浠讹紙濡傜嚎锛夊強浜岀淮绌洪棿鐗╀欢锛堝姝ｆ柟褰級鍦ㄤ笁缁寸┖闂翠腑閮...
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绛旓細鍥犱负姝ｅ叚闈綋6涓潰鍏ㄩ儴鐩哥瓑锛屼笖鍧囦负姝ｆ柟褰紝鎵浠ユ鏂逛綋琛ㄩ潰绉叕寮忎负锛歋 = 6 * a * a锛屽叾涓紝a涓烘鍏潰浣撶殑妫遍暱锛孲涓烘鍏潰浣鐨勮〃闈㈢Н銆傚浘涓殑姝ｆ柟浣撴１闀挎槸2dm锛岄偅涔堟牴鎹叕寮忓緱姝ｆ柟浣撹〃闈㈢НS = 6 * a * a = 6 * 2 * 2 = 24锛堝钩鏂瑰垎绫筹級銆
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