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.

Correct result:

r =  0.4301 dm
h =  2.1506 dm

Solution:

$$\begin{gathered} V=1.25\text{ l}\to {\text{dm}}^3=1.25\cdot 1{\text{dm}}^3=1.25{\text{dm}}^3 \\ h=5r \\ V=\pi r^{2}h \\ V=\pi r^{2}5r \\ V=5\pi r^3 \\ r=\sqrt[3]{V\mathrm{/}(5\pi )}=\sqrt[3]{1.25\mathrm{/}(5\cdot 3.1416)}=0.4301\text{ dm} \end{gathered}$$

$h=5\cdot r=5\cdot 0.4301=2.1506\text{ dm}$

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