Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

l is 45

Answer 8

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

Answer 9

i got 15

Answer 10

correct, good job

Answer 11

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.

Answer 12

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

Answer 13

basexheight

Answer 14

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

Answer 15

pir^2

Answer 16

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

Answer 17

multiply 8*pi
divide on both sides

Answer 18

78.5

Answer 19

dont forget about pi (use3.14)
r^2 = 78.5/pi
divide 78.5/3.14
then take the square root to get r

Answer 20

4.99

Answer 21

correct

Answer 22

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

Answer 23

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.

Answer 24

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

Answer 25

so that mean 22

Answer 26

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

Answer 27

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

Answer 28

7.00

Answer 29

good
next we use volume of cone formula

Answer 30

so that i use 1/3bh

Answer 31

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.

Answer 32

yes
b = area of circle w/ radius of 7

Answer 33

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

Answer 34

49pi

Answer 35

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

Answer 36

with pi?

Answer 37

yes

Answer 38

256.56

Answer 39

good now round to nearest foot

Answer 40

257

Answer 41

don't forget your units

Answer 42

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

Answer 43

thanks kristo, forgot about that

Answer 44

no problem

Answer 45

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?

Answer 46

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

Answer 47

1080

Answer 48

one sec i will be right back...

Answer 49

ok i'm back

Answer 50

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

Answer 51

i drew what next

Answer 52

okay so what you have is a rectangular prism with a base of 6x12 (the smallest face) making the height without water 15

Answer 53

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

Answer 54

that make 72

Answer 55

720 6x12x10 remember to include WxLxH

Answer 56

then

Answer 57

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

Answer 58

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

Answer 59

hint: largest face

Answer 60

12 and 10

Answer 61

12 and 15

Answer 62

180

Answer 63

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

Answer 64

use the volume formula we found before 720

Answer 65

720=15x12xH

Answer 66

i got 4 for height

Answer 67

great

Answer 68

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

Answer 69

2

Answer 70

yes

Answer 71

do you really understand how we got that?

Answer 72

well some of the time

Answer 73

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

Answer 74

does that help to picture the problem a little better?

Answer 75

yes so BxH

Answer 76

yes!

Answer 77

or length times width times height = volume

Answer 78

but you got the concept

Answer 79

i have to sleep now but good luck

Answer 80

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