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How do I answer this question? A hemispherical dome holds a volume of 486 pi ft^3. Find...

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hardworking-h... | eNoter

Posted June 9, 2013 at 3:53 PM via web

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How do I answer this question?

A hemispherical dome holds a volume of 486 pi ft^3. Find the surface area(omit the area of the circle).

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 9, 2013 at 4:24 PM (Answer #1)

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You should use the equation that gives the area of the hemisphere, such that:

`SA = 2*pi*r^2`

`r` represents the radius of hemisphere

The problem provides the volume of hemisphere, hence, you need to use the formula of volume to evaluate the radius, such that:

`V = (2/3)*pi*r^3`

Replacing `486` for V yields:

`486 = (2/3)*pi*r^3 => 729 = pi*r^3 => r^3 = 232.047 => r = root(3)(232.047) => r = 6.145`

Replacing `6.145` for r in formula of surface area yields:

`SA = 2*pi*6.145^2 = 237.259 ft^2`

Hence, evaluating the surface area of hemispherical dome, under the given conditions, yields `SA = 237.259 ft^2.`

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