Question

15. The diameter of a circular park is 74 m. A uniform path 3 m wide runa around outside. Find the
cost of levelling the path at 15.50 per sq metre. ​

Answer 1

Given -

The diameter of a circular park is 74 m. A uniform path 3 m wide runs around outside.

To find -

• The cost of levelling the path at 15.50 per sq metre.

Solution -

• Diameter of a circular park = 74 m
• Radius of circle = 74/2 = 37 m

A uniform path 3 m wide runs around outside.

• Inner radius (r) = 37 m
• Outer radius (R) = 37 + 3 = 40m

Area of circular park

→ Area of outer radius - area of inner radius

→ πR² - πr²

→ π(R² - r²)

• Apply identity
• a² - b² = (a + b)(a - b)

→ π[(R + r)(R - r)]

• Substitute the value of "r" and "R"

→ 22/7[(40 + 37)(40 - 37)]

→ 22/7 × 77 × 3

→ 22 × 11 × 3

→ 726 m²

Rate of levelling the circular path is Rs.15.50

→ Total cost of levelling

→ 726 × 15.50

→ Rs.11253

•°• Total cost of levelling the circular path is Rs.11253

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Answer 2

$\large\underline{\red{\sf \orange{\bigstar} Given:-}}$

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• ➪ As diameter is 74 m

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• ➪ Radius =40m

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$\large\underline{\pink{\sf \red{\bigstar} To Find:-}}$

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• ➪ cost of levelling the path ?

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$\large\underline{\orange{\sf \green{\bigstar} Solution:-}}$

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• ➪ Area=22/7 × r × r

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• ➪ 22/7 × 40 ×40

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• ➪ 5024 m^2

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Radius minus path=47-3

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$\large\underline{\pink{\sf \red{\bigstar} .}}$44m$\large\underline{\pink{\sf \blue{\bigstar} .}}$

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• ➪ New area= 22/7 ×37 ×37

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• ➪ 4,298.66 m^2

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• ➪ Area of path=5024- 4298.66

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• ➪ $\purple{\sf{\star\;725.34\; m^2}}$

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• ➪ Cost of leavening path=725.66×15.50

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➪11,247.73 ${\boxed{\green{\checkmark{}}}}$

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$\large\underline{\pink{\sf \green{\bigstar} .}}$Note

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• Diagram is in attachment!!

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