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LekaFEV [45]
3 years ago
14

A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. find the height and radius of the cup that will use the

smallest amount of paper. (round your answers to two decimal places.)
Mathematics
1 answer:
alekssr [168]3 years ago
6 0
The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm
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