Axial section

The axial section of the cylinder is diagonal 45 cm long, and we know that the area of the side and the base area are in ratio 6:5.

Calculate the height and radius of the cylinder base.

Correct answer:

h =  12.93 cm
r =  21.55 cm

Step-by-step explanation:

$$\begin{gathered} u=45\text{cm} \\ 45^2=h^2+(2r{)}^2 \\ \frac{S_1}{S_2}=6:5=\frac{6}{5} \\ \frac{2\pi rh}{\pi r^2}=\frac{6}{5} \\ \frac{2h}{r}=\frac{6}{5} \\ r=\frac{2\cdot h\cdot 5}{6} \\ {r}^2=h^2+16h^2\cdot 5^2/6^2=h^2(1+16\cdot 5^2/6^2) \\ h=\frac{u}{\sqrt{1+16\cdot 5^2/6^2}}=\frac{45}{\sqrt{1+16\cdot 5^2/6^2}}=12.93\text{cm} \end{gathered}$$

$r=\frac{2\cdot h\cdot 5}{6}=\frac{2\cdot 12.9307\cdot 5}{6}=21.55\text{cm}$

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