Thread: Estimating error using differentials

Use differential to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a hemispherical dome with diameter 50cm.


S= 2 pi r^2

ds= 4 pi r dr.

r= 50/2= 25 cm

dr= 0.05cm

So ds= 4 pi 25*0.05= 5 pi cm^2

Originally Posted by camherokid

Use differential to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a hemispherical dome with diameter 50cm.


S= 2 pi r^2

ds= 4 pi r dr.

r= 50/2= 25 cm

dr= 0.05cm

So ds= 4 pi 25*0.05= 5 pi cm^2

i may be wrong, but isn't the amount of paint talking about volume?

So the answer must be this :

V= 2/3* pi r^3

dV= 2 pi r^2 dr.

r= 50/2= 25 cm

dr= 0.05cm

So dV= 2 pi 25^2*0.05= 62.5 pi cm^3

Originally Posted by camherokid

So the answer must be this :

V= 2/3* pi r^3

dV= 2 pi r^2 dr.

r= 50/2= 25 cm

dr= 0.05cm

So dV= 2 pi 25^2*0.05= 62.5 pi cm^3

yup, that looks about right