Question

a conical container has a height of 20cm and a base diameter of 12cm. It holds water a depth of 10cm above its vertex. Find the volume of its content.

Answer 1

Ok I got this, volume for conical container is V = 1/3 pi r2 h

V=1/3(pi)(6^2)(20)

Volume approximately equals 753.98

Answer 2

753.98cm

Answer 3

wait, can I ask why did you use the 20cm?

Answer 4

and the answer's not in the choices. :(

Answer 5

because that was the height you gave

Answer 6

but it also gave me 10cm. what is that for?

Answer 7

i tried that with the same givens before but gave me the wrong answer too :(

Answer 8

is 251.32 one of your answers?

Answer 9

that's a no too

Answer 10

I think you need the formula for the volume of a frustum
Here's the formula:
Frustum Volume = (π • height • (Ra2 + Ra • Rb + Rb2) ÷ 3)
and here's a link to my web page:
http://www.1728.org/volcone.htm

Answer 11

In order to use that formula we have to calculate the radius of the circle at 10 cm height

Base radius = 6
height = 20 cm

Answer 12

wait should i use 10 as height or 20?

Answer 13

I was busy making a graphic.
We need to calculate the length of the red line.

Answer 14

Is the calculation as easy as taking one half of 6?
The length of the red line is 3 ?

Answer 15

I get volume of 659.73
is that one of the choices?

Answer 16

no :( haha

Answer 17

i tried to use 3 and 10 in the volume formula and i got the answer. lol

Answer 18

but im not sure if its right

Answer 19

but its in the choices

Answer 20

no? wow I thought that was it.
I used 3 and 6 for the radii and height of 10

Answer 21

i thought so too. haha. do you know any other ways to get the upper radius?

Answer 22

If you don't mind, what are the answers?

Answer 23

the choices are 20 30 40 60, all with pi (e.g 20pi)

Answer 24

The biggest answer is 60*PI which is about 188.5 which isn't even half of the answer I gave.
Is the problem stated corrrectly?
Height 20
Halfway 10
base radius =6
top radius = 3

Answer 25

yup that's correct. but we dont know the top radius if its really 3

Answer 26

I'd say it is 3

Answer 27

what if the conical section is upside down? so the content would be from the tip and only one radius? haha

Answer 28

that's what i though when i used 3 and 10 lol

Answer 29

It holds water a depth of 10cm above its vertex does this means something else?

Answer 30

I always thought the vertex was the absolute top point of a cone , triangle, etc.
Maybe I'll see what wikipedia says.

Answer 31

yup that's right but you know, just some outside thinking. haha

Answer 32

Yes, it's what I said - the absolute top point of a cone.

Answer 33

By the way, I just tried 2 calculations to fine the volume
volume of a 20 cm hgt 6cm radius cone 753.98
volume of a 10 cm hgt 3cm radius cone 94.248

Subtracting 1 from the other = 659.732

Hmm that looks familiar!!! LOL

Answer 34

haha! are we close to the answer? LOL

Answer 35

no I don't think we are any closer. But at least you know HOW to find the volume.

Answer 36

By the way, why did you pick 1018 as a user name?

Answer 37

wait, what do you mean. i know how to get volume. lol

just random numbers. to stay anonymous. haha. i like your though. because wolf. nice.

Answer 38

Thanks - and the 1728 (besides the name of my website) is also 12 cubed
= 12^3 =
12*12*12
1,728

Answer 39

nice nice! mathematical. hahaha

Answer 40

Absolutely!!!
By the way, feel free to use my website all you want. It has a lot more than just cone calculators. If you are taking algebra geometry rig, etc you;ll find all calculators to help you.

Answer 41

that "rig " should be trig LOL

Answer 42

haha hey thanks!

Answer 43

Okay, you are welcome.
Well, think I should go.
Good luck with those math problems.

Answer 44

Thanks for the medal!!

Answer 45

no problem!

Answer 46

Okay see ya!!