Hectoliters - tank

A cylindrical tank with a base diameter of 1.2 m is supposed to hold 17 hectoliters of water. How many square meters of sheet metal are needed to make it? We calculate if 2% of the surfaces are for joints and waste.

Correct answer:

S =  8.09 m²

Step-by-step explanation:

$$\begin{gathered} d=1.2\text{m} \\ V=17\text{hl}\to {\text{m}}^3=17:10{\text{m}}^3=1.7{\text{m}}^3 \\ q=100\%+2\%=1+\frac{2}{100}=1.02 \\ r=d/2=1.2/2=\frac{3}{5}=0.6\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.6^2\doteq 1.131{\text{m}}^2 \\ V=S_1\cdot h \\ h=V/S_1=1.7/1.131\doteq 1.5031\text{m} \\ {S}_2=\pi \cdot d\cdot h=3.1416\cdot 1.2\cdot 1.5031=\frac{17}{3}\doteq 5.6667{\text{m}}^2 \\ {S}_3=2\cdot S_1+S_2=2\cdot 1.131+5.6667\doteq 7.9286{\text{m}}^2 \\ S=q\cdot S_3=1.02\cdot 7.9286=8.09{\text{m}}^2 \end{gathered}$$

Try another example