Question

Answer the following Design-A: Brooch A is made with silver wire in the form of circle with diameter 28mm.
The wire used for making 4 diameters which divide the circle into 8 equal sectors.
Design-B : Brooch B is made in two colours-Gold and Silver. Outer part is made with
gold. The circumference of silver part is 44mm and the Gold part is 3mm wide
everywhere.
Refer to design-A
i) The total length of the silver wire required is
a) 180mm b) 200mm c) 250mm d) 280mm
ii) The area of each sector of the brooch is
a) 44mm2
b) 52mm2
c) 77mm2
d) 68mm2
Refer to design-B
iii) The circumference of outer part (Golden) is
a) 48.49mm b) 82.22mm c) 72.50mm d) 62.86mm
iv) The difference of areas of Golden and Silver parts is
a) 18π b) 44π c) 51π d) 64π
v) A boy is playing with the brooch B. He makes revolution with it along its edge. How
many complete revolutions must it take to cover 80π mm.
a) 2 b) 3 c) 4 d) 5

Answer 1

Given:

Design-A:

Brooch A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal sectors.

Design-B :

Brooch B is made in two colours-Gold and Silver. The outer part is made of gold. The circumference of the silver part is 44mm and the Gold part is 3mm wide everywhere.

To find:

Refer to design-A

i) The total length of the silver wire required is?

ii) The area of each sector of the brooch is?

Refer to design-B

iii) The circumference of the outer part (Golden) is?

iv) The difference of areas of Golden and Silver parts is?

v) A boy is playing with the brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80π mm.?

Solution:

Referring to Design-A:

(i). Finding the total length of the silver wire:

Diameter = 28 mm

∴ Radius = $\frac{28}{2} = 14 \:mm$

Thus,

The total length of the silver wire used is,

= [Circumference of the circular brooch A] + [4 × Diameters]

= [$2 \pi r$] + [4 × Diameters]

= [$2 \times \frac{22}{7} \times 14$] + [4 × 28]

= 88 + 112

= $\boxed{\bold{200\:mm}}$ ← option (b)

(ii). Finding the area of each sector of the brooch A:

The area of each sector of the brooch A is,

= $\frac{Area \:of\:the\:circular\:brooch\:A}{no.\:of\:sectors}$

= $\frac{\pi r^2}{8}$

= $\frac{\frac{22}{7} \times 14^2}{8}$

= $\frac{616}{8}$

= $\boxed{\bold{77\:mm^2}}$ ← option (c)

Referring to Design-B:

Circumference of the silver part = 44 mm

⇒ $2\pi \times radius \:of\: the \:silver \:part= 44$

⇒ $Radius \:of\: the \:silver \:part= \frac{44 \times 7}{2 \times 22}$

⇒ $Radius \:of\: the \:silver \:part= 7\:mm$

The width of the golden part = 3 mm

∴ The radius of the golden part = 7 + 3 = 10 mm

(iii). Finding the circumference of the outer golden part:

The circumference of the outer golden part is,

= $2 \pi r$

= $2 \times \frac{22}{7} \times 10$

= $\boxed{\bold{62.86\:mm}}$ ← option (d)

(iv). Finding the difference of areas of Golden and Silver parts:

The difference of areas of Golden and Silver parts is,

= $\pi$ [(Radius of golden part)² - (Radius of the silver part)²]

= $\pi [10^2 - 7^2]$

= $\pi [100 - 49]$

= $\boxed{\bold{51\pi\:mm^2}}$ ← option (c)

(v). Finding the no. of revolutions:

Let "n" represents the no. of revolution the brooch B must make to cover 80$\pi$ mm.

We know,

Circumference of brooch B = Distance covered in 1 revolution = $2\pi \times 10$

∴ n = $\frac{Total \:distance \:covered}{Circumference} = \frac{80\pi}{2\pi \times 10} = \frac{80\pi}{20\pi } = 4$

Thus, it must take → option (c) → $\boxed{\bold{4}}$ complete revolutions to cover 80$\pi$ mm.

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Also View:

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(i) the total length of the silver wire required.

(ii) the area of each sector of the brooch.

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Answer 2

Step-by-step explanation:

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