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# A fez, the cap used by the Turks, is shaped like the frustum of a cone (see figure). 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.

"

Given:

A fez, the cap used by the Turks, is shaped like the frustum of a cone.

Its radius on the open side is 10 cm, its radius at the upper base is 4 cm and its slant height is 15 cm.

To do:

We have to find the area of material used for making it.

Solution:

Radius of the open side $(r_1) = 10\ cm$

Radius of the upper base $(r_2) = 4\ cm$

Slant height of the cone $(l) = 15\ cm$

This implies,

Curved surface area of the frustum $=\pi(r_{1}+r_{2}) l$

$=\pi(10+4) 15 \mathrm{~cm}^{2}$

$=\frac{22}{7} \times 14 \times 15 \mathrm{~cm}^{2}$

$=22 \times 2 \times 15 \mathrm{~cm}^{2}$

$=660 \mathrm{~cm}^{2}$

The surface area of the upper base $=\pi r_{2}^{2}$

$=\frac{22}{7} \times 4 \times 4$

$=50.28 \mathrm{~cm}^{2}$

The total surface area of the cap $=$ Curved surface area of the frustum $+$ Area of the upper base

$= 660+ 50.28$

$= 710.28\ cm^2$

**The area of material used for making it is $710.28\ cm^2$.**

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