Decimeters 83242

The axial section of the cylinder is a square with a content of 56.25 cm². Calculate its surface area and volume. Express the result in square decimeters and cubic decimeters and round to hundredths.

Correct answer:

S =  2.65 dm²
V =  0.3313 dm³

Step-by-step explanation:

$$\begin{gathered} S_1=56.25{\text{cm}}^2\to {\text{dm}}^2=56.25:100{\text{dm}}^2=0.5625{\text{dm}}^2 \\ a=\sqrt{S_1}=\sqrt{0.5625}=\frac{3}{4}=0.75\text{dm} \\ a=2r=d \\ r=a/2=0.75/2=\frac{3}{8}=0.375\text{dm} \\ h=a=0.75=\frac{3}{4}=0.75\text{dm} \\ {S}_2=\pi \cdot r^2=3.1416\cdot 0.375^2\doteq 0.4418{\text{dm}}^2 \\ {S}_3=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 0.375\cdot 0.75\doteq 1.7671{\text{dm}}^2 \\ S=2\cdot S_2+S_3=2\cdot 0.4418+1.7671=2.65{\text{dm}}^2 \end{gathered}$$

$V=S_2\cdot h=0.4418\cdot 0.75=0.3313{\text{dm}}^3$

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