Axial section

The axial section of the cylinder has a diagonal 40 cm. The shell size and base surface are in the ratio 3:2.

Calculate the volume and surface area of this cylinder.

Correct answer:

S =  3855.98 cm²
V =  15473.44 cm³

Step-by-step explanation:

$$\begin{gathered} 40^2=h^2+(2r{)}^2 \\ \frac{S_1}{S_2}=\frac{3}{2} \\ \frac{2\pi rh}{\pi r^2}=\frac{3}{2} \\ \frac{2h}{r}=\frac{3}{2} \\ r=\frac{2h\cdot 2}{3} \\ {r}^2=h^2+16h^2\cdot 2^2/3^2=h^2(1+16\cdot 2^2/3^2) \\ h=\frac{40}{\sqrt{1+16\cdot 2^2/3^2}}=14.045cm \\ r=\frac{2h\cdot 2}{3}=18.727cm \\ S=2\pi r^2+2\pi rh=3855.98{\text{cm}}^2 \end{gathered}$$

$V=\pi r^{2}h=15473.44{\text{cm}}^3$

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