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. [Use π = 22/7.]
Given: Radius of lower circular end = R = 10 cm
Radius of upper circular end = r = 4 cm
Slant height = l = 15cm
Formula: Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2
As the lower circular end is open we need to subtract the area of lower circular end from total surface area since we don’t require material for lower circular end it should be open so that it is wearable.
∴ Total surface area = πr2 + πR2 + π(R + r)l- πR2 cm2
= (22/7) × (42 + (10 + 4) × 15) cm2
= (22/7) × (16 + 210) cm2
= 22 × 226/7 cm2
= 710.285 cm2
∴ total surface area = 710.285 cm2
∴ Area of material used = 710.285 cm2