Q. 204.7( 12 Votes )

# 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.]

Answer :

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 = πr^{2} + πR^{2} + π(R + r)l cm^{2}

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 = πr^{2} + πR^{2} + π(R + r)l- πR^{2} cm^{2}

= (22/7) × (4^{2} + (10 + 4) × 15) cm^{2}

= (22/7) × (16 + 210) cm^{2}

= 22 × 226/7 cm^{2}

= 710.285 cm^{2}

∴ total surface area = 710.285 cm^{2}

∴ Area of material used = 710.285 cm^{2}

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