My biggest problem
A cylindrical container is filled with ice cream whose diameter is 12cm, and height is 15cm. The whole ice cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice cream cone.
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1 solution
Let the radius of the base of conical ice cream = x cm
•Diameter=2x cm
•Then, height of the conical ice cream =2(diameter) = 2(2) = 4x cm
•Volume of ice cream cone = Volume of conical portion + Volume of hemispherical portion
=1/3 πr^{2}h + 2/3πr^{3}
=2πx^{3} cm^{3}
•Diameter of cylindrical container= 12 cm
Its height(h)= 15 cm
• Volume of cylindrical container=πr^{2}h
= 540π cm^{3}
•No. Of children to whom ice cream is distributed =10
•Volume of cylindrical container/ Volume of one ice cream cone= 10
540π/2πx^{3} = 10
x^{3} = 27
x. = 3
!!!!!!!!!!!!!!!!!!!!!!!!!!DIAMETER OF ICECREAM CONE 2x= 2(3) = 6 cm!!!!!!!!!!!!!!!!!!!!!!!!!!