Estimate Paint Amount for Hemispherical Dome w/ Differentials

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SUMMARY

This discussion focuses on estimating the amount of paint required for a hemispherical dome using differentials. The diameter of the dome is 46 meters, leading to a radius of 23 meters. The volume differential is calculated using the formula dv = 2π(23m)²(0.0003m), resulting in an estimated paint volume of 0.3174 m³, which rounds to 0.32 m³. The initial error in the calculation was due to the omission of π in the formula.

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Micah2
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Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 46 m. (Round your answer to two decimal places.)

First I list what I am given:
Diameter: 46m
DR: 0.0003m (converted from the 0.03cm that was given)
DV: ?

Volume of a Sphere = 4/3 pi r^3
But volume of a half a Sphere = 2/3 pi r^3
And Radius = Diameter/2

So...dv = 2 pi (23m)^2 (0.0003m)

Using a Calculator I am given 0.3174. The question asks to round it to two decimal places, which would be 0.32.
All homework is done online but apparently this answer is still incorrect. I appreciate all and any help to sort this out. :(
 
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you forgot the $\pi$ ...
 

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    hemisphere_dV.png
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skeeter said:
you forgot the $\pi$ ...

Doh! Yes, that did the trick. Thank you so much! :)
 

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