From a right circular cylinder of radius 10 cm × height 21 cm a right circular cone of same base radius is removed. If the volume of the remaining portion is 4,400cm3, then the height of the cone removed is
15 cm
18 cm
21 cm
24 cm
A
15 cm
B
21 cm
C
18 cm
D
24 cm
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Solution
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Volume of, cylinder =π(10)221=2, 100πcm3 If h be the height of the cone, then Volume of cone =13π(10)2h=1003πhcm3 By hypothesis, 2100π−1003πh=4,400 ⇒(6300−100h)π=13,200 ⇒6,300−100h=13,200×722=4,200 ⇒100h=6,300−4,200=2,100 ⇒h=21 cm
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