A sidewalk is to be constructed around a pool that measures #(10.0+-0.1) m# by #(17.0+-0.1) m#. If the sidewalk is to measure #(1.00+-0.01) m# wide by #(9.0+-0.1) cm# thick, what volume of concrete is needed and what is its approximate uncertainty?
1 Answer
Area of the pool
Area of pool
(sidewalk is
Area of sidewalk
Volume of concrete needed for the sidewalk
We know that
Volume
#V=lxxbxxt#
Taking
#logV=log(lxxbxxt)#
#=>logV=logl+logb+logt#
From theory of errors
#(DeltaV)/V=(Deltal)/l+(Deltab)/b+(Deltat)/t#
where#DeltaV# stands for error or uncertainty in volume and similarly for other terms.
Inserting given values we get
Errors/uncertainties are always taken as additive
In terms of % uncertainty