Estimate Paint for Hemispherical Dome - Linear Approximation

[josesalazmat]

Hello
I have tried to resolve the problem below

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.040000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

My procedure was:

the volume of the sphere is $$V=4/3 pi r^3$$ but this is a hemispherical dome, so the formula should be $$V=2/3pir^3$$

I derived it, so
$$dv=2pir^2 * dr$$

dr is 0.04000 cm
the radius is 22.5
Then, the result should be 127.17 cm ^3 but this result is showed as wrong
I don't know where I am making the mistake
I will appreciate any advice

Thanks

 

[skeeter]

Hello
I have tried to resolve the problem below

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.040000 cm thick to a hemispherical dome with a diameter of 45.000 meters.

My procedure was:

the volume of the sphere is $$V=4/3 pi r^3$$ but this is a hemispherical dome, so the formula should be $$V=2/3pir^3$$

I derived it, so
$$dv=2pir^2 * dr$$

dr is 0.04000 cm
the radius is 22.5
Then, the result should be 127.17 cm ^3 but this result is showed as wrong
I don't know where I am making the mistake
I will appreciate any advice

Thanks

I get 127.23 $cm^3$ ... did you use 3.14 for pi? I used my calculator's approximation for pi.

Maybe an exact solution? ... $\dfrac{81\pi}{4} \, cm^3$