1.

A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Answer» Please refer to video for the figure.
Area of material used for making fez, `A` = Curved Surface Area of frustum + Area of circular part at the top of fez
So, `A = pi**(r_1+r_2)**l +pir_2^2`
Here, `l = 15, r_1 = 10 and r_2 = 4`
Putting these values,
`A = pi(10+4)**15+pi**16=226**22/7 ~= 710.6cm^2`


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