calculate the area of the sand pit.

Question

a children's stand pit is bordered by railway sleepers so that each side is 2 metres long. all corners are right angles. the plan of the sand pit is in a plus symbol shape. the pit is filled with sand to a uniform depth of 300mm.

 

can someone please show me how to do this?

 

what is the area of the sand pit?

what is the volume of sand in the sand pit?

sand costs $35 per cubic metre. how much does it cost to fill the sand pit?

Answer 1

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Did the best I could to provide a crude representation of the sand pit.  They say that it is bordered by railway sleepers, so that each side is 2 meters long.  So each singular side of the cross is 2 meters.  To find the area, you can break it up into separate pieces.  I'd recommend doing squares.  Each portion of the cross is a square the top, the left, the right, and the bottom, with one more square right in the middle of all the other ones for a total of 5 squares.

 

Since every side is 2 meters long, the area of 1 square is 4 m².  Multiply that by 5 and we have 20 m².

 

To find the volume, we must multiply the area by the depth of the sand pit, which is 300mm, however, we must first convert the mm to regular meters, since 1000mm = 1 m, 300mm = .3 m.

 

So we multiply our 20 m² by .3 m and we get 6 m³ which is now our volume.

 

If it costs $35 per cubic metre, we multiply that by the 6 m³, and the cost is $210.