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

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novjb | (Level 1) Salutatorian

Posted September 17, 2013 at 7:45 PM via web

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A hemispherical dome holds a volume of 486 (pi) cubic ft. Find the surface area (omit the area of the circle).
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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 17, 2013 at 8:20 PM (Answer #1)

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The volume of a hemisphere with radius r is given by;

`V = 2/3pir^3`

Since the volume is `486pift^3` ;

`486pi = 2/3pir^3`

`r = ((486xx3)/2)^(1/3)`

`r = 9ft`

Area of hemisphere `= 2pir^2`

Area of hemisphere `= 2xxpixx9^2 = 162pift^2`

So the area of the hemisphere is `162pift^2` .

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