A right circular cone is of height 3.6 cm and radius of its base is 1.6 cm . It is melted and recasted into a right circular cone with radius of its base 1.2 cm. Find the height of the cone so formed.
A
6.4 cm
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B
6 cm
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C
4 cm
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D
4.8 cm
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Solution
The correct option is A6.4 cm As the cone is melted and recasted in to another cone, Volume of both the cones are equal. Volume of a cone V=13πr2h, where r is the radius of the base of the cone and h is the height. Let h be the height of the new cone formed.
Given, in original cone, height h=3.6cm and radius r=1.6cm.
Also, in new cone, radius r=1.2cm. Now, V1=V2 Thus 13π×1.62×3.6=13π×1.22×h ⇒h=6.4 cm.