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Centroids - volume of a solid revolution: a firm which imports new motor cars....


New member
Mar 9, 2017
I have calculated the centroid of the cross section of the road but after i have mapped the coordinates on a graph the road is not a quater circle and am struggling with what to do.

“AB Cars,” is a firm which imports new motor cars. The Company has acquired a plot of land alongside Jones Road. On this site they require an access road to be provided for the delivery of vehicles, a large storage compound, office accommodation and a distribution centre where the cars will be prepared for sale at showrooms throughout Britain. The proposed layout is shown on the plan attached. (Not to scale.)

Taking coordinates from the origin given in the diagram (all units in metres):

Access road width 7.2m, inner radius 35m, centre (50, 0, 0)

Storage compound 50mx35m (40, 20, 0), (40, 55, 0), (90, 55, 0), (90, 20, 0)

Offices wall height 3m,
(90,20,0), (90,55,0), (104.5,55,0), (104.5,33.3,0), (114,33.3,0), (114,20,0)

The architect has incorporated a cross fall to the surface of the carriageway, in order to shed surface water. Calculate the volume of carriageway concrete required, if the depth of the slab is 325mm at one side and 200mm at the other.

  • a clear explanation of the strategy used to calculate the volume of concrete, is required.
  • the effect the choice of angle has on total volume, should be stated. The problems have been solved correctly and their accuracy considered. Checking procedures should be included.
State any assumptions made,