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, then find the area of material used for making it.

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To solve this problem use π=22/7

Problem from RS Aggarwal book, problem number 20, page number 824, exercise 17C, chapter volume and surface area of solid.

solution

given data

Radius of open side, R=10 cm

Radius of upper base, r=4 cm

Slant height, l=15 cm

The area of material used=π[R+r]l+πr²

= [22/7] × [10+4] × 15 + [ [22/7] × 4 × 4

=[22/7] ×14×15 + [[22/7]×4×4]

= [22/7]×210+16

= [22/7] × 226

= 4972/7 cm²

= 710.28 cm²

∴ the area of material used for making the fez is 710.28 cm²