Cylindrical 38791

The cylindrical barrel is 1.2 m high, and the diameter of its base is 0.6 m. How many hectoliters of water will fit in the barrel? What is the smallest amount of sheet metal needed for its production? (we count both bases)

Correct answer:

V =  3.3929 hl
S =  2.8274 m²

Step-by-step explanation:

$$\begin{gathered} h=1.2\text{m} \\ D=0.6\text{m} \\ r=D/2=0.6/2=\frac{3}{10}=0.3\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.3^2\doteq 0.2827{\text{m}}^2 \\ {V}_1=S_1\cdot h=0.2827\cdot 1.2\doteq 0.3393{\text{m}}^3 \\ V=V_1\to \text{hl}=V_1\cdot 10\text{hl}=0.3393\cdot 10\text{hl}=3.393\text{hl}=3.3929\text{hl} \end{gathered}$$

$S=2\cdot S_1+2\pi \cdot r\cdot h=2\cdot 0.2827+2\cdot 3.1416\cdot 0.3\cdot 1.2=2.8274{\text{m}}^2$

Try another example