Question

I NEED HELP ASAP
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 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

@supie

Answer 2

Do you know the formula for volume for a cylinder and a cone? @leviisshort

Answer 3

wdym by that?

Answer 4

all the info i have is in the question...

Answer 5

Do you know how to calculate the volume of a cylinder?

Or the volume of a cone?

I'm guessing you don't so here:

Volume for cylinder = \(\pi r^2h\)

Volume for cone = \(\dfrac{1}{3} \pi r^2h\)

Answer 6

what do you notice that is different between the two formulas?

Answer 7

the 1/3

Answer 8

Exactly!! So that means if we have the same radius (which is r) and the same height (which is h in the equation)

that means a cone would have 1/3 the volume of that of a cylinder

Answer 9

do you want to use the numbers that they gave you to prove that?

`diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.`

Answer 10

yes please

Answer 11

so they gave us the diameter

how do we calculate the radius?

remember, to find the radius just divide the diameter by 2

Answer 12

so if the diameter is 8, what is the radius?

Answer 13

4? i remember the radius being half of the diameter

Answer 14

not 100% sure tho

Answer 15

exactly!

Answer 16

so now we have radius = r = 4

and they told us
height = 5 for the cylinder

and
radius = 4
height = 15 for the cone

Answer 17

so let's first focus on the cylinder

volume = πr2h

we said for the cylinder, r = 4 and h = 5
(and we can use 3.14 for \(\pi\)

so put the numbers in

volume = 3.14 * (4)^2 * 5

Answer 18

251.2?

Answer 19

Yes

Answer 20

and id cut that into thirds or..?

Answer 21

is that just my answer

Answer 22

no so that was for your cylinder, let's take a look at the cone now, okay?

Answer 23

ok

Answer 24

the cone had a diameter of 8 which we said is the same thing as a radius of 4

but the cone has a height of 15

Answer 25

so the cylinders volume is 251.2?

Answer 26

so the formula for volume of a cone is

Volume of cone = \(\dfrac{1}{3} \pi r^2 h\)

Answer 27

yes

Answer 28

so to find the volume for the cone i have to divide that by 3?

Answer 29

If it had the same numbers, we could have

but for the cone, they told us that the height is 15 and not 5 like the cylinder

Answer 30

So let's plug in radius = 4 and height = 15

Volume = 1/3 * pi * (4)^2 * 15
Volume =

Answer 31

i got 251.32? idk if thats right it sounds weird

Answer 32

It is!

Answer 33

So remember how we said that if BOTH the radius and height were the same

the volume of a cone would be 1/3 of that of a cylinder

Answer 34

ya

Answer 35

but this time, what they did was they gave you the same radius BUT the height of the CONE was 3 times the height of the cylinder

Answer 36

so the 1/3 cancelled out with the 3 times the height to give you the same volume for both

Answer 37

does that make sense?

Answer 38

mhm

Answer 39

thank u :D

Answer 40

No problem!! :D