Question

a sector shape handfan made by cloth as shown in figure radius and angle .type of fan are 21cm abd 120 degree the find the required cloth and used fence of wire​

Answer 1

Given:

A hand-made fan which is in the shape of a sector of a circle of radius 21 cm and of angle 120°, is made up of cloth

To find:

(i) Area of the cloth used  

(ii) The total length of the wire

Solution:

(i) Finding the area of the cloth used:

The radius of the sector of the circle, r = 21 cm

The measure of the central angle, θ = 120°

Here to get the area of the cloth used, we have to find the area of the sector.  

So, we know the formula of the area of a sector when θ is given in terms of degrees is given as,

$\boxed{Area\:of\:sector = \frac{\theta}{360}\times\pi r^2 }$

By substituting the given values in the formula, we get

$Area\:of\:sector = \frac{120}{360}\times\frac{22}{7} \times 21^2 = 462\: cm^2$

Thus, the area of the cloth used is 462 cm².

(ii) Finding the total length of the wire:

We will first find the arc length of the hand-made fan i.e.,

$Arc\: Length = \frac{\theta}{360} \times 2\pi r= \frac{120}{360} \times 2\times \frac{22}{7}\times 21 = 44 cm$

Now,

The required length of the wire is given by,

= sum of all sides of the hand-made fan

= [2 × radius] + Arc length

substituting the value of radius and arc length

= [2 × 21] + 44

= 42 + 44

= 86 cm

Thus, the total length of the wire required to make such a fan is 86 cm.

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