Lampshade fabric calculation

Lampshade for the face of a truncated cone with a height of 20 cm. The upper diameter of the shade is 13 cm, the lower 36 cm, and the side forms an angle of 60 degrees with the lower diameter. At least how much fabric is needed to make this shade?

Final Answer:

S =  1775.7 cm²

Step-by-step explanation:

$$\begin{gathered} D_1=13\text{cm} \\ {D}_2=36\text{cm} \\ {r}_1=D_1/2=13/2=\frac{13}{2}=6.5\text{cm} \\ {r}_2=D_2/2=36/2=18\text{cm} \\ h=20\text{cm} \\ s=\sqrt{h^2+(r_2-r_1{)}^2}=\sqrt{20^2+(18-6.5{)}^2}\doteq 23.0705\text{cm} \\ S=\pi \cdot (r_1+r_2)\cdot s=3.1416\cdot (6.5+18)\cdot 23.0705=1775.7{\text{cm}}^2 \end{gathered}$$

Try another example