heather040200
Help! I give medals:) pic below
Find the volume.A hemispherical tank has a total surface area of 243pi squared(this includes the circular base area).Show work
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heather040200
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|dw:1368065262840:dw|
heather040200
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@e.mccormick @timo86m @knock @mathslover think one of u could help me out plezz :)
timo86m
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what is the formula for area of a sphere?
heather040200
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v=4/3pir^3
timo86m
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it's A=4*Pi*r^2 but you want half
so
2pi r^2=A
solve for r :)
timo86m
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2pi r^2=A
A/(2 pi)=r^2 divide both sides by 2pi
sqrt(A/(2 pi))=r take sqrt of both sides
plug in the area in A :)
sqrt((243*pi^2)/(2 * pi))=r
knock
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I think you should include the surface of the circular base, doesn't?
timo86m
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i get like 19.5
heather040200
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me to n the surface area they gave me is 243pi squared
heather040200
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then do i do SA=1/24pir^2
heather040200
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and v=1/2pi cubed
e.mccormick
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Did you remember the base in the surface area formula?
heather040200
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is it S=B+1/2Cl=pir squared+pirl
razor99
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@ heather the volume of a hemisphere is
2/3 pi r^2
heather040200
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volume=253.5??
razor99
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I mean the formulae
heather040200
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so is the volume 253.5??
razor99
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me?
heather040200
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ya ig
razor99
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I guess so
e.mccormick
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I got a very different number.
e.mccormick
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Find the volume. A hemispherical tank has a total surface area of 243pi squared (this includes the circular base area). Show work
Therefore:
Half SA of Sphere + A of base = 243
SA Sphere = \(4\pi r^2\)
A of Circle = \(\pi r^2\)
\[\frac{1}{2}4\pi r^2+\pi r^2=243\\
\implies 3\pi r^2=243\\
\implies \pi r^2=81\\
\implies r^2=\frac{81}{\pi}\\
\implies r=\frac{9}{\sqrt{\pi}}\]
Did you follow that for finding the radius?
razor99
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To radius I get 4.39
so when it get round off to 2 decimal its 4.40
razor99
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This is the volume 356.19
e.mccormick
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Or just leave it with the root of pi since that will partially cancel in the next step when doing area. Always save constant conversion until the last step for greater accuracy.
e.mccormick
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@razor99 r=4.39? How?