A hemisphere has a volume of 18π cm3. Find its radius

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A hemisphere has a volume of 18π cm3. Find its radius

Mathematics
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Volume is half that of a sphere V=(1/2)*(4/3)*pi*r^3 = 18pi -> 2/3 r^3 = 18 ->r^3 = 18*(3/2) -> r^3 = 27 = 3*3*3 r=3
A sphere has a volume of 972π in.3. Find its radius.
same as above V = 4/3 pi r^3 = 972 solve for r

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A triangular pyramid has a volume of 180 cm3 and a height of 12 cm. Find the length of a side of the triangular base if the triangle’s height from that side is 6 cm.
volume of pyramid is area of base(B)*height V = B*12 = 180 B = 180/12 = 15 Area of base is area of triangle A = 1/2 * length(L)*height = 15 1/2*6*L = 15 solve for L
oops i messed up volume of pyramid is 1/3* B*h correction 1/3*B*12 = 180 B = 180/4 = 45 ... A=1/2*6*L = 45
l is 45
no (1/2)*6*L = 45 solve for L by multiplying 6 and 1/2, then dividing on both sides
i got 15
correct, good job
The volume of a cylinder is 628 cm3. Find the radius of the base if the cylinder has a height of 8 cm. Round your answer to the nearest 0.1 cm.
ok for this one can you tell me the volume formula for cylinder?
basexheight
good base is a circle, whats the area of a circle?
pir^2
good V = (pir^2)*h pi*r^2*8 = 628
multiply 8*pi divide on both sides
78.5
dont forget about pi (use3.14) r^2 = 78.5/pi divide 78.5/3.14 then take the square root to get r
4.99
correct
actually with rounding to nearest .1 it would just be 5
Sylvia has just discovered that the valve on her cement truck failed during the night and that all the contents ran out to form a giant cone of hardened cement. To make an insurance claim, she needs to figure out how much cement is in the cone. The circumference of its base is 44 feet, and it is 5 feet high. Calculate the volume to the nearest cubic foot.
to answer this we need to find radius what is circumference of circle
so that mean 22
good but we still need to divide by pi (3.14)
2pi*r =44 pi*r=22 r=22/pi
7.00
good next we use volume of cone formula
so that i use 1/3bh
really all you need to do to solve these problems is just write out the sets of equations that apply to the problem for example the circumference equation and the volume of a cone. then, you plug in what you know such as the measurement of circumference to solve for the radius then plug that into the volume of a cone formula.
yes b = area of circle w/ radius of 7
use what you do know to find what you don't
49pi
good V = 1/3 * 49pi*5 multiply it out
with pi?
yes
256.56
good now round to nearest foot
257
don't forget your units
yep ok i gotta go keep doing these steps, find correct formula plug in numbers you you solve for ones you don't good luck
thanks kristo, forgot about that
no problem
A sealed rectangular container 6 cm by 12 cm by 15 cm is sitting on its smallest face. It is filled with water up to 5 cm from the top. How many centimeters from the bottom will the water level reach if the container is placed on its largest face?
alright first you need to find the volume of the water on its smallest face
1080
one sec i will be right back...
ok i'm back
so what might be a good idea is to draw a picture first which face would be the smallest?
i drew what next
okay so what you have is a rectangular prism with a base of 6x12 (the smallest face) making the height without water 15
so the height of the water is five cm from the top so you subtract five from fifteen to get the height of the water
that make 72
720 6x12x10 remember to include WxLxH
then
now we have the volume what we don't know is what the height of the water is when the container is set on its largest face
so i would draw a picture of the new rectangle first what is the W and the L of the base?
hint: largest face
12 and 10
12 and 15
180
we only subtracted five to find the height of the water when the container was on the small face, since we have the W and L now we solve for the height using the volume formula V=WxLxH
use the volume formula we found before 720
720=15x12xH
i got 4 for height
great
now subtract that from six since it wants the height from the top of the prism
2
yes
do you really understand how we got that?
well some of the time
try to image a cereal box, you have the box standing up. you know how high the cereal is from the top of the box you use that to find the volume of the cereal. then you tip the box on its larger face then you want to know what the height of the cereal is from the new top edge of the box
does that help to picture the problem a little better?
yes so BxH
yes!
or length times width times height = volume
but you got the concept
i have to sleep now but good luck
we know that 4 is the height so we need to find the base

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