Question

A sidewalk is to be constructed around a swimming 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 (6.0 ± 0.2 ) cm thick, what volume of concrete is needed? (Use the correct number of significant figures in your answer.) What is the approximate uncertainty of this volume?

Answer 1

Given above, where A=area, L=length, W=width, p=pool, s=sidewalk
Ap = Lp*Wp = (17)(10.0) = 170 m²
A = L*W = (Lp+2Ws)(Wp+2Ws)
= (17+2)(10.0+2) = 228 m²
As = A - Ap = 58 m²
Vs = As*Hs = (58)(0.060) = 3.48 m³

Now lets fully expand the volume formula then plug in max. dimensions:
Vs = As*Hs = Hs(A-Ap)
Vs = Hs((Lp+2Ws)(Wp+2Ws)-(Lp*Wp))
= (0.062)((17.1+2*1.01)(10.1+2*1.01) - (17.1*10.1)) = 3.65 m³

So uncertainty (tolerance) =
(Vmax-Vnom)/Vnom = (3.65-3.48)/3.48 = 4.8%