# Surface area of the top

A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.

Result

S =  31.416 cm2

#### Solution:

$u=20 \ \text{cm} \ \\ h=3D \ \\ u^2=h^2 + D^2 \ \\ u^2=9D^2 + D^2 \ \\ D=\dfrac{ u }{ \sqrt{ 9+1 } }=\dfrac{ 20 }{ \sqrt{ 9+1 } } \doteq 2 \ \sqrt{ 10 } \ \text{cm} \doteq 6.3246 \ \text{cm} \ \\ r=D/2=6.3246/2 \doteq \sqrt{ 10 } \ \text{cm} \doteq 3.1623 \ \text{cm} \ \\ h=3 \cdot \ D=3 \cdot \ 6.3246 \doteq 6 \ \sqrt{ 10 } \ \text{cm} \doteq 18.9737 \ \text{cm} \ \\ u_{2}=\sqrt{ h^2 + D^2 }=\sqrt{ 18.9737^2 + 6.3246^2 }=20 \ \text{cm} \ \\ u=u_{2} (check - ok) \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 3.1623^2 \doteq 31.4159 \ \\ S=10 \ \pi=31.416 \ \text{cm}^2$

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