What is the Cost of Painting a Vessel with Given Dimensions?

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The discussion revolves around calculating the total cost of painting a hollow steel hemispherical vessel with inner and outer radii of 2 cm and 3 cm, respectively, at a rate of 70 cents per cm². The correct approach involves calculating the total surface area, which includes the curved surface area and the rim area. The formula for the total surface area combines the curved surface area of the hemisphere and the area of the rim. Participants confirm the necessity of including the rim area in the calculation to arrive at an accurate cost. The conversation highlights the importance of thoroughness in mathematical problem-solving.
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Homework Statement



The inner and outer radii of a hollow steel hemispherical vessel are 2 cm and 3 cm respectively.what is the total cost of painting the vessel all over at the rate of 70 cents per cm² ?



[ b]2. Homework Equations [/b]
Curved surface area of hemisphere=2[pi]*[radius]²

The Attempt at a Solution


total Surface area= 2[pi]*{[inner radius]² + [outer radius]²}
TOTAL cost = 0.7*total Surface area

is it right?
 
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Yes, but you can't forget about the rim, with area PI ( [outer radius]^2 - [inner radius]^2 )
 
csprof2000 said:
Yes, but you can't forget about the rim, with area PI ( [outer radius]^2 - [inner radius]^2 )

u got a point.i was just falling short of the answer by an iota. Thanks buddy.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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