A cubic meter of sand is ordered. The sand is poured into a sandpit but there is too much. If the sand pit is 2m square and 18cm deep and the extra sand makes a mountain above the edges
a) estimate the h, the height of the top of the sand above the ground
To estimate the height of the extra sand above the edges, we need to first calculate the volume of the sandpit.
The sandpit has dimensions of 2m x 2m x 0.18m (depth) = 0.72 cubic meters.
The extra sand that makes a mountain above the edges is the difference between the volume of the sand ordered (1 cubic meter) and the volume of the sandpit (0.72 cubic meters) which is 1 - 0.72 = 0.28 cubic meters.
Now, we need to find the height of the top of the sand above the ground. Since the sand is poured evenly into the sandpit, we can assume that the extra sand forms a pyramid on top of the sandpit.
The volume of a pyramid is given by the formula V = (1/3) x base area x height.
The base area of the pyramid is the same as the base area of the sandpit, which is 2m x 2m = 4 square meters.
So, 0.28 = (1/3) x 4 x h
0.28 = (4/3) x h
h = 0.28 x (3/4)
h = 0.21 meters
Therefore, the estimated height of the top of the sand above the ground is approximately 0.21 meters.