Question

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. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

Radius on the open side of the frustum of a cone $=r_1=10cm$

Radius at the upper base $=r_2=4cm$

Slant height $=l=15cm$

Area of the material used for making cap = curved surface area + Area of the upper base

$=\pi (r_1+r_2)l+\pi .{r_2}^2=\left(\frac{22}{7}\right(10+4)\times 15)+(\frac{22}{7}\times 4^2)$

$=660+\frac{352}{7}$

$=\frac{4972}{7}c{m}^2$

$=710\frac{2}{7}c{m}^2$