anonymous
  • anonymous
A hemisphere has a volume of 18π cm3. Find its radius
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
dumbcow
  • dumbcow
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
anonymous
  • anonymous
A sphere has a volume of 972π in.3. Find its radius.
dumbcow
  • dumbcow
same as above V = 4/3 pi r^3 = 972 solve for r

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anonymous
  • anonymous
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.
dumbcow
  • dumbcow
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
dumbcow
  • dumbcow
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
anonymous
  • anonymous
l is 45
dumbcow
  • dumbcow
no (1/2)*6*L = 45 solve for L by multiplying 6 and 1/2, then dividing on both sides
anonymous
  • anonymous
i got 15
dumbcow
  • dumbcow
correct, good job
anonymous
  • anonymous
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.
dumbcow
  • dumbcow
ok for this one can you tell me the volume formula for cylinder?
anonymous
  • anonymous
basexheight
dumbcow
  • dumbcow
good base is a circle, whats the area of a circle?
anonymous
  • anonymous
pir^2
dumbcow
  • dumbcow
good V = (pir^2)*h pi*r^2*8 = 628
dumbcow
  • dumbcow
multiply 8*pi divide on both sides
anonymous
  • anonymous
78.5
dumbcow
  • dumbcow
dont forget about pi (use3.14) r^2 = 78.5/pi divide 78.5/3.14 then take the square root to get r
anonymous
  • anonymous
4.99
dumbcow
  • dumbcow
correct
dumbcow
  • dumbcow
actually with rounding to nearest .1 it would just be 5
anonymous
  • anonymous
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.
dumbcow
  • dumbcow
to answer this we need to find radius what is circumference of circle
anonymous
  • anonymous
so that mean 22
dumbcow
  • dumbcow
good but we still need to divide by pi (3.14)
dumbcow
  • dumbcow
2pi*r =44 pi*r=22 r=22/pi
anonymous
  • anonymous
7.00
dumbcow
  • dumbcow
good next we use volume of cone formula
anonymous
  • anonymous
so that i use 1/3bh
anonymous
  • anonymous
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.
dumbcow
  • dumbcow
yes b = area of circle w/ radius of 7
anonymous
  • anonymous
use what you do know to find what you don't
anonymous
  • anonymous
49pi
dumbcow
  • dumbcow
good V = 1/3 * 49pi*5 multiply it out
anonymous
  • anonymous
with pi?
dumbcow
  • dumbcow
yes
anonymous
  • anonymous
256.56
dumbcow
  • dumbcow
good now round to nearest foot
anonymous
  • anonymous
257
anonymous
  • anonymous
don't forget your units
dumbcow
  • dumbcow
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
dumbcow
  • dumbcow
thanks kristo, forgot about that
anonymous
  • anonymous
no problem
anonymous
  • anonymous
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?
anonymous
  • anonymous
alright first you need to find the volume of the water on its smallest face
anonymous
  • anonymous
1080
anonymous
  • anonymous
one sec i will be right back...
anonymous
  • anonymous
ok i'm back
anonymous
  • anonymous
so what might be a good idea is to draw a picture first which face would be the smallest?
anonymous
  • anonymous
i drew what next
anonymous
  • anonymous
okay so what you have is a rectangular prism with a base of 6x12 (the smallest face) making the height without water 15
anonymous
  • anonymous
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
anonymous
  • anonymous
that make 72
anonymous
  • anonymous
720 6x12x10 remember to include WxLxH
anonymous
  • anonymous
then
anonymous
  • anonymous
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
anonymous
  • anonymous
so i would draw a picture of the new rectangle first what is the W and the L of the base?
anonymous
  • anonymous
hint: largest face
anonymous
  • anonymous
12 and 10
anonymous
  • anonymous
12 and 15
anonymous
  • anonymous
180
anonymous
  • anonymous
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
anonymous
  • anonymous
use the volume formula we found before 720
anonymous
  • anonymous
720=15x12xH
anonymous
  • anonymous
i got 4 for height
anonymous
  • anonymous
great
anonymous
  • anonymous
now subtract that from six since it wants the height from the top of the prism
anonymous
  • anonymous
2
anonymous
  • anonymous
yes
anonymous
  • anonymous
do you really understand how we got that?
anonymous
  • anonymous
well some of the time
anonymous
  • anonymous
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
anonymous
  • anonymous
does that help to picture the problem a little better?
anonymous
  • anonymous
yes so BxH
anonymous
  • anonymous
yes!
anonymous
  • anonymous
or length times width times height = volume
anonymous
  • anonymous
but you got the concept
anonymous
  • anonymous
i have to sleep now but good luck
anonymous
  • anonymous
we know that 4 is the height so we need to find the base

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