Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm².

Correct result:

V =  19.15 dm³
S =  40 dm²

Solution:

$$\begin{gathered} 24=2\pi rh \\ h:D=3:4 \\ h:r=3:2 \\ 2h=3r \\ 24=3\pi r^2 \\ r=\sqrt{8\mathrm{/}\pi }=1.596dm \\ h={\displaystyle \frac{3}{2}}r=2.394dm \\ V=\pi r^{2}h=19.15{\text{dm}}^3 \end{gathered}$$

$S=24+2\pi r^2=40{\text{dm}}^2$

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