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

- anonymous

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

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- 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

A sphere has a volume of 972π in.3. Find its radius.

- dumbcow

same as above
V = 4/3 pi r^3 = 972
solve for r

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## More answers

- 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

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

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

l is 45

- dumbcow

no
(1/2)*6*L = 45
solve for L by multiplying 6 and 1/2, then dividing on both sides

- anonymous

i got 15

- dumbcow

correct, good job

- 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

ok for this one can you tell me the volume formula for cylinder?

- anonymous

basexheight

- dumbcow

good
base is a circle, whats the area of a circle?

- anonymous

pir^2

- dumbcow

good
V = (pir^2)*h
pi*r^2*8 = 628

- dumbcow

multiply 8*pi
divide on both sides

- anonymous

78.5

- 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

4.99

- dumbcow

correct

- dumbcow

actually with rounding to nearest .1 it would just be 5

- 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

to answer this we need to find radius
what is circumference of circle

- anonymous

so that mean 22

- dumbcow

good but we still need to divide by pi (3.14)

- dumbcow

2pi*r =44
pi*r=22
r=22/pi

- anonymous

7.00

- dumbcow

good
next we use volume of cone formula

- anonymous

so that i use 1/3bh

- 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

yes
b = area of circle w/ radius of 7

- anonymous

use what you do know to find what you don't

- anonymous

49pi

- dumbcow

good
V = 1/3 * 49pi*5
multiply it out

- anonymous

with pi?

- dumbcow

yes

- anonymous

256.56

- dumbcow

good now round to nearest foot

- anonymous

257

- anonymous

don't forget your units

- 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

thanks kristo, forgot about that

- anonymous

no problem

- 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

alright first you need to find the volume of the water on its smallest face

- anonymous

1080

- anonymous

one sec i will be right back...

- anonymous

ok i'm back

- anonymous

so what might be a good idea is to draw a picture first which face would be the smallest?

- anonymous

i drew what next

- 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

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

that make 72

- anonymous

720 6x12x10 remember to include WxLxH

- anonymous

then

- 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

so i would draw a picture of the new rectangle first what is the W and the L of the base?

- anonymous

hint: largest face

- anonymous

12 and 10

- anonymous

12 and 15

- anonymous

180

- 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

use the volume formula we found before 720

- anonymous

720=15x12xH

- anonymous

i got 4 for height

- anonymous

great

- anonymous

now subtract that from six since it wants the height from the top of the prism

- anonymous

2

- anonymous

yes

- anonymous

do you really understand how we got that?

- anonymous

well some of the time

- 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

does that help to picture the problem a little better?

- anonymous

yes so BxH

- anonymous

yes!

- anonymous

or length times width times height = volume

- anonymous

but you got the concept

- anonymous

i have to sleep now but good luck

- anonymous

we know that 4 is the height so we need to find the base

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