Design and Measurement

For our class assignment my group is in charge of Design and Measurement so hear it is.

In the Design and Measurement unit every thing was pretty straight forward. Basically all that you had to do was multiply the amount of material that you were using and multiply it by the price of the material, or if your looking for how much material there is left over you subtract how much you use by the total material used. Vice versa if your looking for how much material you used.

Here is an example.

A ballpark is to be built according to the following diagram.

A fence is to be put up around the entire park.

Fencing costs $1.35 per running foot.

The infield area that is to have shale on it needs to be dug down 18"(inches) so that one foot of gravel can be put down as a base and the 6"(inches) of shale put on top.

The cost of excavation is $9.00 per cubic yard.

Gravel costs $7.00 per cubic yard and shale costs $9.50 per cubic yard.

The remaining area of the park needs to have 4"(inches) of topsoil on it and sod put on top of the soil.

Topsoil costs $20 per cubic yard and sod costs $1.25 per square foot.

The grass needs to have fertilizer as soon as it is laid.

The fertilizer costs $15.60 per bag and a bag will cover 75 square yards.

Find the total cost of this project.

P.S.T. at 7% and G.S.T. at 5% apply to all materials used. Only G.S.T. applies to the excavation cost.

Start off by finding the area of the entire park, the infield and outfield, this will save you some time later on.

Area of entire ballpark is Area=Pi r^2 (Pi radius squared)

     =Pi 240^2

     =180955.7 /4 = 45238.9 feet square

Area or infield is Area=Pi r^2 (Pi radius squared)

      =Pi 125^2

      =49238.4 /4 = 12271.85 feet square

You have to divide these two answers by 4 because you are finding the area of an entire circle and you only want the area of a quarter the entire circle.

To find the outfield area subtract the infield are from the entire ballpark area.

45238.9 - 12271.85 = 32967.05 feet square

Now we can start figuring out the cost of the park.

Cost of Fence- Perimeter = 2Pi r

     = 2Pi 240

     = 1508 /4 = 377 + 2(240) = 857 * $1.35 = $1156.95

Cost of infield

Excavation- Cost = 1.5 * 12271.85 /27 = 681.8 * $9.00 = $6136

When finding the cost of something that is in yards we need to divide by 27 because the area we found is in feet.

Cost of Shale- Cost = 1/2 foot or .5 * 12271.85 = 227.3 * $9.50 = $2159.35

Cost of Gravel- Cost = (1 foot or 1 * 12271.85) /27 = 454.51 * $7 = $3181.57

Cost of Topsoil- Cost = (4 inches/12 inches * 32967.10) /27 = 407 * $20 = $8140

Cost of Sod- Cost = 32967.10 * $1.25 = $41208.88

Cost of Fertilizer- Cost = 32967.10 /27 /75 = 16.3 * $15.60 = $254.30

Now add up all of the purple prices to get a total of $56101.05

Now find the total excavation cost tax included. $6136 * 1.05 = $6442.8

Then find the total material cost plus tax. $56101.05 * 1.12 = $62833.18

Finally add the two totals in red to get your final total of $69275.98