已知扇形的圓心角為120°,面積為300πcm2.
(1)求扇形的弧長;
(2)若將此扇形卷成一個圓錐,則這個圓錐的軸截面面積為多少?
【答案】
分析:(1)根據(jù)扇形面積公式S=
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求得半徑R,再根據(jù)l=
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求弧長;
(2)由1的弧長為底面周長求得底面半徑,由勾股定理求得圓錐的高,再根據(jù)三角形的面積公式求得面積.
解答:
解:(1)∵300π=
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,
∴R=30,
∴弧長L=20π(cm);
(2)如圖所示:
∵20π=2πr,
∴r=10,R=30,
AD=
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=20
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,
∴S
軸截面=
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×BC×AD=
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×2×10×20
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=200
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(cm
2).
答:扇形的弧長是20πcm卷成圓錐的軸截面是200

cm
2.
點評:本題利用了勾股定理,扇形的面積公式,弧長公式,圓周長公式求解.