An oil company distributes oil in a metal can shaped like a cylinder that has an actual radius of 5.1cm and a height of 15.1cm. A worker incorrectly measured the radius as 5cm and the height as 15cm. Determine the relative error in calculating the surface area, to the nearest thousandth.

Question

amistre64 · Answer

compare volumes is what im thinking

amistre64 · Answer

or surface areas as this case may be

amistre64 · Answer

i got no idea what a "relative" error is tho; terminology still eludes me from time to time

anonymous · Answer

Thanks! I'll try to figure it out

amistre64 · Answer

2pi r h + 2pi r^2  is the formula for surface area, that i think i recall correctly

amistre64 · Answer

2pi r(h+r)

anonymous · Answer

SA = 2π r h + 2π r²  
= 2π r ( h + r )  = 2π *5 ( 10 + 5) = 471.24 cm²

SA' = 2π (r' h + r h') + 4π r r'
= 2π ( 10 *.1  + 5 * .1) + 4π * 5 * .1
= 2π *1.5  + 2π  = 15.7  cm²

=> Relative error: 15.7/  471.24 = .0333 = 3%