SOLUTION: A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and
an opening 6 cm wide. If all the ice melted in the cup, would it overflow?
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-> SOLUTION: A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and
an opening 6 cm wide. If all the ice melted in the cup, would it overflow?
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Question 1180543: A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and
an opening 6 cm wide. If all the ice melted in the cup, would it overflow? Answer by math_tutor2020(3817) (Show Source):
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The ball of flavored ice is a sphere of radius r = 4
Volume of Sphere = (4/3)*pi*r^3
Volume of Sphere = (4/3)*pi*4^3
Volume of Sphere = 268.08257
The spherical ice takes up roughly 268.08257 cm^3 of space.
The height of the cone is h = 12
The cone's opening is 6 cm wide, so this represents the diameter. Half that is the radius r = 3.
Volume of Cone = (1/3)*pi*r^2*h
Volume of Cone = (1/3)*pi*3^2*12
Volume of Cone = 113.09734
The paper cone can hold roughly 113.09734 cm^3 of material.
Since the volume of this sphere is larger than this cone, it means that melting all of the ice will lead to overflow.
The amount of overflow is roughly 268.08257-113.09734 = 154.98523 cm^3
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