Question

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wir is also used in making 5 diameters which divide the circle into 10 equal sectors . Find the total length of the silver wire required and the area of each sector of brooch.​

Answer 1

ANSWER ⤵️

Find :

Total length of silver wire required

The Area of Each sector of the brooch

$\underline{\underline{\sf{\maltese\:\:Given}}}$

Diameter of Brooch = 35 mm

The wire is also used in making 5 diameters

Wire divides the circle into 10 equal sectors

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

Total length of silver wire required

The Area of Each sector of the brooch

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Total length of silver wire required = 285 mm

Area of Each sector of the brooch = 96.25 mm²

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

Before going into calculation part, we need to know about some basic terms related to the answer

Diameter :  The diameter is the length of the line through the center that touches two points on the edge of the circle.

Radius :  A line segment extending from the center of a circle or sphere to the circumference

Also :

Diameter = 2 × Radius

Radius = Diameter

First Let's Find

Total length of silver wire required

Total length of silver wire required

= Length of Wire in Circle + Wire Used in 5 diameters

⇒ Total length of silver wire required

= Circumference of Circle + Wire Used in 5 diameters

⇒ Total length of silver wire required = 2πr + Wire Used in 5 diameters

⇒ Total length of silver wire required = 2πr + (5 × Diameter of Circle)

⇒ Total length of silver wire required = 2 × π × r + (5 × Diameter of Circle)

⇒ Total length of silver wire required

= 2 × π × (diameter/2) + (5 × Diameter of Circle)

⇒ Total length of silver wire required

= 2 × π × (35/2 mm) + (5 × Diameter of Circle)

⇒ Total length of silver wire required = 2 × π × (35/2 mm) + (5 × 35 mm)

⇒ Total length of silver wire required = 2 × π × (35/2 mm) + (175 mm)

Since π = 22/7

⇒ Total length of silver wire required = 2 × 22/7 × (35/2 mm) + (175 mm)

⇒ Total length of silver wire required = 2 × 22/7 × 35/2 mm + 175 mm

⇒ Total length of silver wire required = 2 × 22/1 × 5/2 mm + 175 mm

⇒ Total length of silver wire required = 2 × 22 × 5/2 mm + 175 mm

⇒ Total length of silver wire required = 22× 5/1 mm + 175 mm

⇒ Total length of silver wire required = 22 × 5 mm + 175 mm

⇒ Total length of silver wire required = 110 mm + 175 mm

⇒ Total length of silver wire required = 285 mm

Let's Find

The Area of Each sector of the brooch

Area of Each sector of the brooch = Area of Circle/10

⇒ Area of Each sector of the brooch = πr²/10

⇒ Area of Each sector of the brooch = π × r²/10

⇒ Area of Each sector of the brooch = π × (diameter/2)²/10

Since π = 22/7

⇒ Area of Each sector of the brooch = 22/7 × (diameter/2)²/10

⇒ Area of Each sector of the brooch = 22/7 × (35/2 mm)²/10

⇒ Area of Each sector of the brooch = 22/7 × ((35 × 35/(2 × 2)) mm²/10

⇒ Area of Each sector of the brooch = 22/1 × ((5 × 35/(2 × 2))  mm²/10

⇒ Area of Each sector of the brooch = 22 × ((5 × 35/(2 × 2))  mm²/10

⇒ Area of Each sector of the brooch = 22 × ((5 × 35)/(2 × 2)) mm²/10

⇒ Area of Each sector of the brooch = 11 × ((5 × 35)/(1 × 2)) mm²/10

⇒ Area of Each sector of the brooch = 11 × ((5 × 35)/2) mm²/10

⇒ Area of Each sector of the brooch = 11 × (175/2) mm²/10

⇒ Area of Each sector of the brooch = 11 × (175)/(2 × 10) mm²

⇒ Area of Each sector of the brooch = 11 × 175/20  mm²

⇒ Area of Each sector of the brooch = 11 × 8.75 mm²

⇒ Area of Each sector of the brooch = 96.25 mm²

Answer 2

Step-by-step explanation:

Diameter =35mm

∴ Circumference of circle

=2×π×r =2×π×17.5=110mm

i) The total length of the silver wire required

= Circumference of circle + (5×35)

=110+175 = 285mm

(ii) The area of each sector of the brooch

=

Area of circle/10

=

π×17.5×17.5/10

=

$\frac{385}{4} mm {}^{2} =$

96.25 mm² Answer