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A Rectangular Park is 100 M by 50 M. It is Surrounding by Semi-circular Flower Beds All Round. Find the Cost of Levelling the Semi-circular Flower Beds at 60 Paise per Square Metre (Use π = 3.14). - Mathematics

Sum

A rectangular park is 100 m by 50 m. It is surrounding by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (use π = 3.14).

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Solution

Since four semicircular flower beds rounds the rectangular park. Then, diameters of semicircular plots are `2r_1=l and 2r_2=w`

`r_1=l/2`

`=100/2`

`=50 m`

Area of semicircular plot at larger side of rectangle`=1/2 pir^2`

`=1/2xx3.14xx50xx50`

`= 3925 m^2` 

And the radius of semicircle at smaller side of rectangle

`r_2=l/2`

`=50/2`

`=25m`

Area of semicircluar plot at smaller side of rectangle=`1/2 pi r^2`

`=1/2xx3.14xx25xx25`

`=981.25 m^2`

Now, the total area of semicircular plot is sum of area of four semicircular plots.

Total Area of plot`=2xx3925+2xx981.25`

`=7850+192.5m^2`

`= 9812.5 m^2`

Since, The cost of levelling semicircular flower bed per square meter=` Rs 0.60`

So, The  cost of levelling 9812.5 square meter flower bed= `Rs0.60xx9812.5`

      =` Rs  5887.50`

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.4 | Q 10 | Page 56
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