Question

A cone with a radius of 6 cm has a volume of 120π cm3. What is the height of the cone? (The volume of a cone is given by the formula V =
1
3
πr2h.)

Answer 1

try working backwards to find the height

Answer 2

Hey there!

Plug in r = 6 into the equation that you're given for the volume of the cone and v = 120\(\pi\) and solve for h

\(\ V = \frac{1}{3}\pi r^2 h\)

Answer 3

okay thank you!

Answer 4

Let us know what you get and we can check for you!!

Also welcome to QuestionCove!! We're glad to have you here

Answer 5

120pi=1/3pi(6)^2h, then solve for h

Answer 6

I really appreciate
you guys

Answer 7

no problem

Answer 8

I got an 11.2

Answer 9

Can you show us your work or what you put into the calculator?

Answer 10

\(\ 120\pi = \frac{1}{3}\pi (6)^2 h\)

Answer 11

actually I got 10.47

Answer 12

All the stuff on the left hand side are being multiplied so to get rid of them you'd have to divide

So like you'd divide pi on both sides and that would cancel that out

and so on

Answer 13

I did 120/6^2(pi)

Answer 14

so we have 120 pi!
And you forgot the 1/3

So let's do it one step at a time

\(\color{#0cbb34}{\text{Originally Posted by}}\) @TheSmartOne
\(\ 120\pi = \frac{1}{3}\pi (6)^2 h\)
\(\color{#0cbb34}{\text{End of Quote}}\)

What happens when you divide pi on both sides?
Will it cancel out or not?

Answer 15

Yes

Answer 16

Perfect! So now we have

\(\ 120= \frac{1}{3} (6)^2 h\)

Answer 17

What is 6^2 equal to?

Answer 18

36

Answer 19

Good good

Now what is

1/3 * 36

Answer 20

12

Answer 21

Good

So now we have

\(\ 120= 12 h\)

Answer 22

Can you solve for h now?

Answer 23

120/12

Answer 24

Yes and simplify that now

Answer 25

How do I do that?

Answer 26

Well how would you make it smaller

Like what is 120/12

You should be able to do it in your head if you can see 120 is 12*10

Or you could use a calculator

Answer 27

it is 10

Answer 28

Simplify basically means to bring into smaller numbers

So like if you had 24/4
we could "simplify" it to

(12*2) / (2*2)
And we can cross out a 2 from the numerator and denominator

And we get
12/2

But we can simplify it more!!

(6*2) / (2)

And that ultimately is equal to 6

Answer 29

Yes, 10 is correct!!

Answer 30

thank you so so so much

Answer 31

yep good job thats what i got too

Answer 32

Of course!! Hopefully that made sense!

Just remember to next time do it step by step so that way you don't make any silly mistakes

Answer 33

oh yea when you work backwards remember sadmep

Answer 34

I will remember that

Answer 35

Seriously guys thank you so very much

Answer 36

Of course! That's why we're here!

Answer 37

no problem