# Axial section

The axial section of the cylinder has a diagonal 31 cm long, and we know that the area of the side and the base area is in ratio 3:2.

Calculate the height and radius of the cylinder base.

Correct result:

h =  10.88 cm
r =  14.51 cm

#### Solution:

$31^2 =h^2 + (2r)^2 \ \\ \dfrac{S_1}{S_2} = \dfrac{ 3 }{ 2 } \ \\ \dfrac{2\pi r h}{\pi r^2} = \dfrac{ 3 }{ 2 } \ \\ \dfrac{2h}{r} = \dfrac{ 3 }{ 2 } \ \\ r = \dfrac{ 2h\cdot 2 }{ 3 } \ \\ \ \\ r^2 = h^2 + 16 h^2 \cdot 2^2/3^2 = h^2(1+16\cdot 2^2/3^2) \ \\ h = \dfrac{ 31 }{ \sqrt{ 1+16\cdot 2^2/3^2}} = 10.88 \ \text{cm}$
$r = \dfrac{ 2h\cdot 2 }{ 3 } = 14.51 \ \text{cm}$

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