在球心同侧有相距9cm的两个平行截面,它们的面积分别为49πcm2和400π cm2,求球的表面积.
球的表面积为2 500π cm2
如图,为球的轴截面,
由球的截面性质知,AO1∥BO2,且O1、O2分别为两截面圆的圆心,
则OO1⊥AO1,OO2⊥BO2.
设球的半径为R.
∵π·O2B2=49π,∴O2B=7(cm).
同理πO1A2=400π,∴O1A=20(cm).
设OO1=xcm,则OO2=(x+9)cm.
在Rt△OO1A中,R2=x2+202,
在Rt△OO2B中,R2=(x+9)2+72,
∴x2+202=72+(x+9)2,
解得x=15.
∴R2=x2+202=252.
∴R=25(cm).
∴S球=4πR2="2" 500π(cm2).
∴球的表面积为2 500π cm2.
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| The train I was travelling 1 was already half 2 hour late. I had planned to 3 in London at 7:00 4 to catch the 7:50 train to Liverpool, but there was no hope 5 that now. I explained (解释) the situation (情况) to the conductor 6 advised 7 to get off at the stop before London Station and 8 a taxi. When the time came, he even helped me 9 my luggage. He wished me good 10 as I jumped off, and 11 minutes after I was racing towards London Station in a taxi. It was 12 7:50 when we stopped outside the station. I 13 the driver quickly and hurried inside. " The Liverpool train " was all I had time to 14 to the first porter I saw. You can imagine my disappointment when he pointed to a train that was just moving 15 of the station. |
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