Question

a circular field, 28 m in diameter has a path 1.75 m wide running round it on this outside . find the cost of gravelling the path at rs. 5 per square meter..??​

Answer 1

Answer: Rs. 818.125

Step by step explanation:

Radius of circular field (r1) = 14 m

Width of the path = 1.75m

So ,

Radius = 14 + 1.75 = 15.75 m(r2)

Area of circle = πr²

Now, According to question

Area of gravelling the path = Area of circle with r1 - Area of circle with r2

= π (r1)² - π (r2)²

» π [(r1)² - (r2)²]

» π [(15.75)² - (14)²]

» π (248.0625 - 196)

» π (52.0625)

» (22/7) × 52.0625

» 163.625 m²

Thus, Area of the path is 163.625 m².

Now, cost of gravelling per square meter path = Rs.5

So, Cost of gravelling the path

= 163.625 × 5

= Rs. 818.125

Thus, Cost of gravelling the path is Rs.818.125

Answer 2

Answer:

Area of field = $\tt{\pi r^{2}}$

=> $\tt{196 \pi \: m^{2}}$

Area of field + path = $\tt{\pi r^{2}}$

=> $\tt{\pi (14 + 1.75)^{2}}$

=> $\tt{248.0625 \pi \: m^{2}}$

Area of path = $\tt{(248.0625 \pi - 196 \pi )\: m^{2}}$

= $\tt{52.0625 \pi \: m^{2}}$

Cost per metre square = Rs. 5

Cost for $\tt{ 52.0625 \pi \: m^{2}}$ metre square = $\tt{52.0625 \pi \times 5}$

= Rs. 818.125