Question

12. (i) Find the area of the surface of a circular pond
that has a diameter of 12 m.
(ii) The pond is surrounded by a path of width 2 m.
If it costs $55 per m² to pave the path with tiles,
find the cost incurred.​

Answer 1

Given :-

• Diameter od circular pond = 12 m.
• width of path = 2 m .
• cost of paving the path with tiles = $55/m².

To Find :-

• Area of circular pond .
• Total cost .

Solution :-

we know that,

• Area of circle = π * (radius)² .
• Radius = (Diameter/2) .

so,

→ Radius of circular pond = 12/2 = 6 m.

then,

→ Area of the surface of circular pond = 3.14 * 6 * 6 = 113.04 m². (Ans.)

now, given that, width of path is 2 m.

so,

→ Radius of circular pond with path = Radius + width of path = 6 + 2 = 8 m.

then,

→ Area of circular pond with path = 3.14 * 8 * 8 = 200.96 cm².

therefore,

→ Area of path = 200.96 - 113.04 = 87.92 m².

hence,

→ Total cost = Rate * Area of path = 55 * 87.92 = $4835.6 (Ans.)

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