Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter are in a ratio of 3:4, and the area of Lateral Surface Area (LSA) is 24 dm².

Correct answer:

V =  19.15 dm³
S =  40 dm²

Step-by-step explanation:

$$\begin{gathered} h:d=3:4 \\ {S}_2=24{\text{dm}}^2 \\ {S}_2=2\pi rh \\ h:D=3:4 \\ h:r=3:2 \\ 2h=3r \\ 24=3\pi r^2 \\ r=\sqrt{8/\pi }=\sqrt{8/3.1416}\doteq 1.5958\text{dm} \\ h=\frac{3}{2}\cdot r=\frac{3}{2}\cdot 1.5958\doteq 2.3937\text{dm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 1.5958^2=8{\text{dm}}^2 \\ V=S_1\cdot h=8\cdot 2.3937=19.15{\text{dm}}^3 \end{gathered}$$

$S=S_2+2\cdot S_1=24+2\cdot 8=40{\text{dm}}^2$

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