A square park measures 100 m by 50 m. There are semi-circular flower beds all around it. Calculate the cost of leveling of the semi-circular flower beds at 60 paisa per square meter.

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None of the above

answer is A.

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Detailed Solution

Concept: Here, we will use the formula

for the area of a semicircle, which is given by, to determine the total area of semi-circular flower beds.
The rectangular park is 100 meters long.
50 meters is the park's rectangular width.
Question Image

As 1 paisa is equal to Rs. 1100,
The semi-circular flower beds will be leveled for 60 paisa per square meter

each square meter.
The expense of leveling the semi-circular flower beds that surround the park's rectangle is necessary. The amount to level the semi-circular flower beds depends on their overall area.
From the illustration, it is clear that there are four semi-circular flower beds altogether, two of which (A and C) have equal diameters and the other two (B and D), which also have similar diameters, surround the rectangular park. When diameters and radius are equal, areas will likewise be equal as a result.
According to the diagram, semi-circular flower bed A's diameter equals 100 times the park's rectangular length.
As we know that, Radius of a circle

So, Radius of semi-circular flower bed A

Also we know that, Area of a semicircle with a radius R

Area of semi-circular flower bed A

Due to the similar diameters and resulting areas of semi-circular flower beds A and C.
So,

is the size of the semi-circular flower bed C.
Using the figure once again, B's semi-circular flower bed's diameter is equal to the park's 50-meter width.
As we know that, Radius of a circle

So, Radius of semi-circular flower bed B

m
Also we know that, Area of a semicircle with a radius R

Area of semi-circular flower bed B

Due to the similar diameters and resulting areas of semi-circular flower beds B and D.
Therefore, the total area of all the semi-circular flower beds is equal to the sum of the areas of semi-circular beds A, B, C, and D. The area of semi-circular flower bed D is

.
The sum of the areas of semi-circular beds A, B, C, and D makes up the total area of all the semi-circular flower beds.
Total area of semi-circular flower beds is Area of semi-circular flower bed A + Area of semi-circular flower bed B + Area of semi-circular flower bed C + Area of semi-circular flower bed D

Given that the total cost of leveling the semi-circular flower beds equals the rate of leveling them and their combined area
The semi-circular flower beds' overall leveling expense.
Therefore, at 60 paisa per square meter, the total cost of leveling the semi-circular flower beds is

.
Hence, option 1 is correct.

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