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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Answered by
320
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
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
Answered by
107
Answer:
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3 cm
Step-by-step explanation:
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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