# What is the cost of building a 1m wide path that is 10cm thick around a pool 7mx4m if the concrete used costs $129 per m^3.

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A pool with dimensions 7m by 4m is to have a path around it that is 1 m wide. The layer of concrete used for the path has to be 10 cm thick.

The volume of concrete required to build the path is (9*6 - 7*4)*10/100 = (54 - 28)/10 = 26/10 = 2.6 m^3

Concrete costs $129 per m^3.

The cost of 2.6 m^3 of concrete is 129*2.6 = $335.4

**The cost of concrete used to build the path around the pool is $335.4**

sorry to have made an error in the final multiplication

the total cost works up to $335.4

Length of pool = 7m

Breadth of pool = 4m

Since we need a path of width 1m around the pool, the outer borders of the path should extend 1m more on all sides of the pool

so we have path which looks like being made of 4 rectangles

-- the upper and lower ones which are of length 9m and width 1m

--the side ones with length 4m and width 1.

So the total area will be

2* (9*1) +2*(4*1) = 18+ 8 =26m2

T find the perimeter, consider the out ward edges of the path.

The length of the outward edges will be 9m, 4m ,9m and 4m respectively

So the perimeter =9*2+4*2 = 26 m

To find the cost of concrete of depth 10 cm = 0.1 m, we have to find the volume

The longer sides of the path will have volume = 9(length)*1(width)*0.1(depth) = 0.9m3

The shorter sides will have volume = 4*1*0.1 = 0.4m3

so the total volume =0.9*2 +0.4*2 = 1.8 +0.8 = 2.6m3

Cost is $129 per m3

So the total cost is 129 *2.6 = $258