Question 1014234: A road 2m broad surrounds a square park 4225 m^2 in area. Find the cost of paving the marbles each of 25 cm by 8 cm in size on the road at Rs. 50 per piece of marble.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the area of the square park is 4225 square meters.
take the square root of that and you get each side of the park is 65 meters long.
the road surrounding it is 2 meters wide.
if you increase the length of each side by 4 meters (2 on each end), then the length of the new side will be equal to 69 meters.
this new side will include the width of the road on each end.
square this and you get 69^2 = 4761 square meters.
your new area includes the park plus the road.
subtract the area of the park and you get 4761 - 4225 = 536 square meters.
since the road is 2 meters wide, then the length of this road will be 536 / 2 = 268 meters.
you have a road that, if you stretched it out in a straight line, would be equal to 2 meters wide by 268 meters long.
your marble tiles are 8 centimeters wide by 25 centimeters long.
convert that to meters and your marble tiles are .08 meters wide by .25 meters long.
take 268 meters long and divide that by .25 meters long and you get 1072 stones long.
take 2 meters wide and divide that by .08 meters wide and you get 25 stones wide.
1072 stones long by 25 stones wide = 26,800 stones in total.
you could have solved it the following way as well.
the width of the park is 65 meters.
add 2 meters on each end to get a width of 69 meters.
the road is 2 meters wide, so the road along the width and beyond by 2 meters on each side is equal to 2 meters wide by 69 meters long.
your tiles are .08 meters wide by .25 meters long.
2/.08 = 25 stones wide.
69/.25 = 276 stones long.
total stones on the lower road is 25 * 276 = 6900 stones.
same on the upper road gets you a total of 6900 * 2 = 13,800 stones required for the upper and lower road.
on the left side of the park, your road will be 2 meters wide by 65 meters long.
2 meters wide / .08 meters wide = 25 stones wide.
65 meters long / .25 meters long = 260 stones long.
total stones required for the left road is 25 * 260 = 6500 stones.
add the same amount of stones for the right road and you get 2 * 6500 = 13,000 stones for the left and right road.
lower and upper road plus left and right road = 13,800 + 13,000 = 26,800 stones.
you get the same number of stones either way.
see the following diagram for what i mean.
if the cost is 50 per stone, then your total cost for the stones will be 26,800 * 50 = 1,340,000 rs.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A road 2m broad surrounds a square park 4225 m^2 in area. Find the cost of paving the marbles each of 25 cm by 8 cm in size on the road at Rs. 50 per piece of marble.
With area of park being 4,225 sq m, one side of square park =  , or 65 m
Area of entire structure:  , or  , or  , or 4,761 sq m
Area of road: 4,761 – 4,225, or 536 sq m ------> 536(100 * 100), or 536(10,000) = 5,360,000 sq cm
Number of stones needed:  , or  , or 26,800
Cost to pave: 26,800 stones * rs. 50 = 
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