Question

A circular garden with radius 42 m is surrounded from
outside by a path of 3.5 m wide. Find the cost to pave the
stones on the path at the rate of Rs. 20 per m2.

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Answer 1

Answer:

Internal radius = 21 m, External Radius

= 21 + 3.5 = 24.5 m

Area of path = π (24.5)2 - π (21)2

= π [(24.5)2 - (21)2]

= 500.5

Cost of travelling = 500.5 × 4 = 2002

Answer 2

Given :-

• Radius of circular garden = 42m

Width of circular path outside the garden = 3.5m

Aim :-

• To find the cost of paving stones on the path @ ₹20 per m².

Answer :-

Formula to use :

$\boxed { \sf area \: of \: a \: circle = \pi \times radius^{2} }$

• Area of path = (Area of external circle) - (Area of internal circle)

Area of external circle :

• Radius = 42 + 3.5 = 45.5m

Using the formula,

$\implies \sf area = \dfrac{22}{7} \times 45.5 \times 45.5$

Reducing to the lowest terms,

$\implies \sf area = 22 \times 6.5 \times 45.5$

$\implies \sf area = 6506.5 {m}^{2}$

Area of internal circle :

• Radius = 42m

Using the formula,

$\implies \sf area = \dfrac{22}{7} \times 42 \times 42$

Reducing to the lowest terms,

$\implies \sf area = 22 \times 6 \times 42$

$\implies \sf area = 5,544{m}^{2}$

Area of path :

(Area of external circle) - (Area of internal circle)

→ 6506.5m² - 5544m²

→ 962.5m²

Cost of paving :

The cost of paving the path will be :

(Cost of paving the path @ per m²) × (Area of the path)

→ ₹20 × 962.5m²

→ ₹19250

Hence the cost of paving the path will be ₹19250.

More formulas :

• Perimeter of circle = 2 × π × radius
• Area of triangle = ½ × base × height
• Area of parallelogram = base × height
• Area of square = side × side → (side)²
• Area of rectangle = Length × breadth
• Area of rhombus = ½ × Diagonal1 × Diagonal2
• Area of trapezium = ½ × height × (sum of parallel sides)