a cylinder with radius and height 4cm and 8cm are filled with ice cream and ice cream is distributed to 10 children in equal hemispherical tops . if the height of the conical portion is 4 times the radius of its base, find the radius of ice cream cone
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Secondary SchoolMath 8 points
A cylindrical container is filled with ice-cream, whose radius is 6 cm and height is 15 cm. The whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical in equal cones having hemispherical tops. If the height of the conical portion is 4 times the radius of the base, find the radius of the ice-cream cone.
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santy2
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Volume of ice cream = 3.142 x 6² x 15 = 1696.68
Each child gets = 1696.68/10 = 169.668 cm³
Take radius of cone = r = radius of hemisphere
Height of cone is therefore = 4r
Volume of hemisphere + volume of cone = 169.668 cm³
2/3 x 3.142 x r³ + 1/3 x 3.142 x r² (4r) = 169.668
2.09r³ + 4.19r³ = 169.668
6.28r³ = 169.668
r³ = 27
r = 3 cm
∴ Radius of cone = 3 cm
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