Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

@jim_thompson5910

Answer 2

Volume of a Cone
\[\Large V = \frac{1}{3}\pi*r^2*h\]
---------------------------------------
Volume of Cylinder
\[\Large V = \pi*r^2*h\]
----------------------------------------
V = volume
pi = 3.14 approximately
r = radius
h = height

Answer 3

ok...

Answer 4

do those formulas look familiar?

Answer 5

yes..

Answer 6

ok tell me what you get for the volume of the cylinder

Answer 7

ok...

Answer 8

whats the radius and height?

Answer 9

`A cylinder and a cone have the same diameter: 8 inches.`
diameter = 8
radius = 4 (cut the diameter in half to get the radius)

Answer 10

ok!

Answer 11

`The height of the cylinder is 9 inches`

Answer 12

i got v=452.16

Answer 13

`i got v=452.16`
me too

Answer 14

now find the volume of the cone

Answer 15

ok... but for the steps on how i found that answer..

Answer 16

what about them specifically?

Answer 17

well can you tell me the steps you got to find the answer of v=452.16

Answer 18

you tell me. Give it a shot and post what you think

Answer 19

ok ill try!

Answer 20

sorry, give me a sec.. @jim_thompson5910

Answer 21

take your time

Answer 22

thx :)

Answer 23

V=3.14×16×9
V=452.19

Answer 24

@jim_thompson5910

Answer 25

good, before that I would have these steps

V = pi*r^2*h
V = 3.14*4^2*9

Answer 26

so all together, your steps would look something like this

V = pi*r^2*h
V = 3.14*4^2*9
V=3.14*16*9
V=452.19

Answer 27

btw I think you mean to say 452.16

Answer 28

so all together, your steps would look something like this

V = pi*r^2*h
V = 3.14*4^2*9
V=3.14*16*9
V=452.16

Answer 29

oh yes i did sorry.. perfect! is this the complete answer for that question :)

Answer 30

V = pi*r^2*h
V = 3.14*4^2*9
V=3.14*16*9
V=452.16

Answer 31

?

Answer 32

That only takes care of the cylinder. Now you have to do the cone.

Answer 33

ok..

Answer 34

whats the radius and height of the cone?

Answer 35

it's given in the instructions

Answer 36

ok!

Answer 37

4 and 18?

Answer 38

correct on both

Answer 39

13×3.14×16×18=301.44

Answer 40

it's 1/3 and not 13

Answer 41

sorry i forgot to put the 1/3

Answer 42

volume of cone

V = (1/3)*pi*r^2*h
V = (1/3)*3.14*4^2*18
V = (1/3)*3.14*16*18
V = 301.44

Answer 43

ok awesome! now what?

Answer 44

volume of cylinder
V = 452.16

volume of cone
V = 301.44

Divide the two values (big over small)

Answer 45

ok!

Answer 46

i got 1.5

Answer 47

me too

Answer 48

ok so ....

Answer 49

`What is the relationship between the volume of this cylinder and this cone?`
the volume of the cylinder is 1.5 times bigger than the volume of the cone

Answer 50

ok perfect!

Answer 51

so the complete answer for that question is :::

The volume of the cylinder is:
V = pi*r^2*h
V = 3.14*4^2*9
V=3.14*16*9
V=452.16

The Volume of the cone is:
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*4^2*18
V = (1/3)*3.14*16*18
V = 301.44

452.16 / 301.44=1.5
The volume of the cylinder is 1.5 times bigger than the volume of the cone.

Answer 52

@jim_thompson5910

Answer 53

I would add in one thing

Answer 54

The volume of the cylinder is:
V = pi*r^2*h
V = 3.14*4^2*9
V=3.14*16*9
V=452.16

The Volume of the cone is:
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*4^2*18
V = (1/3)*3.14*16*18
V = 301.44


(volume of cylinder)/(volume of cone) = 452.16 / 301.44=1.5
The volume of the cylinder is 1.5 times bigger than the volume of the cone.

Answer 55

ok perfect!!!

Answer 56

omg! yay we're done :)
your the best you know!

Answer 57

glad to be of help