Math, asked by ykuldeep1143, 11 months ago

The cost of painting of semicircular sign board at the rate of 15 paise is rps 49.50.If the diameter of internal semi circle is 28 cm, then find the breath of the sign board.

Answers

Answered by bhagyashreechowdhury
1

The breadth or the width of the signboard is 0.98 cm.

Step-by-step explanation:

Total cost of painting the sign board = Rs. 49.50

The rate of painting the sign board = 15 paise = Rs. 0.15

∴ The area of the semicircular sign board = \frac{49.50}{0.15} = 330 cm²

Let the external radius of the semicircular sign board be "R" cm.

So, we have

Area of the sign board = 1/2 × π R²

⇒ 330 = 1/2 × 22/7 × R²

⇒ 660 = 22/7 × R²

⇒ R = √[30 × 7]

R = 14.49 cm

∴ The diameter of the external semi circle = 2×R = 14.49 × 2 = 28.98 cm

The diameter of internal semicircle is given as 28 cm

Thus,

The breadth or the width of the sign board is given by,

= [diameter of the external semi circle] - [diameter of internal semicircle]

= 28.98 - 29

= 0.98 cm

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Also View:

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(i)the area of the shaded region

(ii)the cost of painting the shaded region at the rate of 25 paise per cm² , to the nearest rupee.

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A wooden plank is in the shape of a square surmounted by a semi-circle on a side. The cost of plank is 50 paise per cm square and the total cost of the piece of the plank is Rs 136.50. Find the perimeter of the plank. (pie = 22/7)

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Answered by ankit8355
2

The breadth or the width of the signboard is 0.49 cm.

Step-by-step explanation:

Total cost of painting the sign board = Rs. 49.50

The rate of painting the sign board = 15 paise = Rs. 0.15

∴ The area of the semicircular sign board = \frac{49.50}{0.15}

0.15

49.50

= 330 cm²

Let the external radius of the semicircular sign board be "R" cm.

So, we have

Area of the sign board = 1/2 × π R²

⇒ 330 = 1/2 × 22/7 × R²

⇒ 660 = 22/7 × R²

⇒ R = √[30 × 7]

⇒ R = 14.49 cm

Therefore, Width of signboard = (External Radius - Internal Radius)

Width of signboard = 14.49 - 14

Width of signboard = 0.49 cm

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