Bottle

A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.

Result

r =  0.43 dm
h =  2.15 dm

Solution:

V=1.25 l=1.25 1 dm3=1.25 dm3 h=5r V=πr2 h V=πr25r V=5 πr3  r=V/(5π)3=1.25/(5 3.1416)30.43010.43 dmV=1.25 \ l=1.25 \cdot \ 1 \ dm^3=1.25 \ dm^3 \ \\ h=5r \ \\ V=\pi r ^2 \ h \ \\ V=\pi r ^2 5r \ \\ V=5 \ \pi r^3 \ \\ \ \\ r=\sqrt[3]{ V/(5 \pi)}=\sqrt[3]{ 1.25/(5 \cdot \ 3.1416)} \doteq 0.4301 \doteq 0.43 \ \text{dm}
h=5 r=5 0.4301=4320=2.15 dmh=5 \cdot \ r=5 \cdot \ 0.4301=\dfrac{ 43 }{ 20 }=2.15 \ \text{dm}



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