Find the surface area

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Find the surface area

Mathematics
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and this
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hello for the first one you need to use formula for SA of sphere and then plug in the radius so what is SA of a sphere? what is the radius of our sphere?

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so i have to divide 1.8 by 2
correct because radius is half the diameter
i got 0.9
now substitute that in for r in SA formula
ok i am doing it right now
i did the volume then i got 0.972pi
correct for volume i thought we were doing surface area
yea but my homework say to find both of them
oh ok what would SA be then
3.24pi
good job for next one do the same thing except at the end we will divide by 2 because its only half a sphere
what do you mean?
it shows image of half sphere with radius of 12 right? so find volume and SA using same formulas substituting 12 for r but we only want half the volume and half the SA
i find the volume is 1152pi
correct
SA is 432pi right?
no i get 288pi SA = 4pi*12^2 = 4pi*144 = 576pi take half of 576 288
ok thank here the another question: The shaded circle at right has area 40π cm2. Find the surface area of the sphere.
i dont understand how are the circle and sphere related?
here the hint:The surface area of a sphere is how many times the area of a circle with the same radius?
ok so they share the same radius is the entire circle shaded?
here the picture
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ok thanks use area of circle formula to find radius, then plug that into SA formula A = pi*r^2 = 40pi
i have to divide pi in both side
yes
i find the raidus 6.32455532
correct
SA=4pi*(6.32)^2
159.7pi
correct and you can round up to 160 since we rounded the radius
Find the volume of a sphere whose surface area is 64π cm2.
first find radius 4pi*r^2 = 64pi
4
good now use that to find volume V = 4/3pi*r^3
i got 256pi over 3
correct
Find the surface area of a sphere whose volume is 288π cm3.
same thing we just did except use volume formula to find radius V = 4/3pi*r^3 = 288pi
what should i do with 4/3 pi?
well first get rid of pi by dividing pi on both sides like last time then we will divide by 4/3
x by 3/4 by both side
correct
what about 288*3/4
think of it as (288*3)/4
i got 6 as radius
correct put that in SA formula
144pi
correct
if the radius of the base of a hemisphere (which is bounded by a great circle) is r, what is the area of the great circle? What is the total surface area of the hemisphere, including the base? How do they compare?
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you can do this one, its just using the formula for circle area and SA the radius is just r
ok i will but i need to leave right but i tell you when i get home
k
ok i'm back so my homewprk paper has Agreat cicrle=,Shemisphere= and SA Hemisphere=__xA of great circle
yes lets fill in the gaps A = area circle SA = area circle + 1/2 SA of sphere
the area of that is pir^2
good A = pir^2
we know the radius is r so that mean..
whats SA of sphere
4pir^2
good SA hemishere = pir^2 +(1/2)*4pir^2 add like terms
3pir^2
good and A = pir^2 right? so SA = ___ * A
what the of Agreat cicrle= and Shemisphere=
i forgot to put answer
A = pir^2 SA hemishere = pir^2 +(1/2)*4pir^2 add like terms
so that is the answer or i have to solve it
no thats the answer, remember we dont know what r is
oh ok so SA = r * A
well does that sense? sub in what we know SA = 3pir^2 and A=pir^2 3pir^2 = r*pir^2 is that true?
not really
ok look at it this way SA = 3pir^2 if i plug in A for pir^2 i get SA = 3A
oh now i got it If Jose used 4 gallons of wood sealant to cover the hemispherical ceiling of his vaction home, how many gallons of wood sealant are needed to cover the floor?
ok use what we just learned SA = 3A = 4 gal + gal for the floor
rid of a and 5 gal
sorry i was unclear there we dont know num of gall for the floor, lets call it x
ok
we know SA of top is 2*pir^2 SA = 2pir^2 = 2A
2A = 4 gall
then divide by 2
A = 2 gal
yes
total = 3A A = 2 gall so total = 3*2 = 6 gallons
i got it thank you so much
your welcome
if i need help for my homework can u help me
yeah if you post it and im on sure
thank again ^_^ that help me a lot from you

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