Question

The volume of a cylinder is 81 cubic feet. What is the volume of a cone that fits exactly inside the cylinder? Provide an explanation and proof for your answer to receive full credit.

Answer 1

@eliassaab @ganeshie8

Answer 2

@eliassaab

Answer 3

@ganeshie8 @UnkleRhaukus

Answer 4

sorrry i don't know but ur queastion is terriffic

Answer 5

it ok

Answer 6

can you get someone to help me please

Answer 7

we know that :-
\[\large \bf Vol.~of~ cone=\frac{1}{3}Vol.~of~ cylinder\]
so,
\[\large \bf Vol.~of~cylinder=3 \times Vol.~of~cone\]

Answer 8

now,can you solve it ? @prowrestler

Answer 9

let me try

Answer 10

sure

Answer 11

just apply this formula :-
\[\huge \bf Vol.~of~cone=\frac{1}{3} \times Vol.~of~cylinder\]

Answer 12

and plug all the values in that formula

Answer 13

@mayankdevnani .. i guess i said the same thing.. just a little over..ur comment..

Answer 14

yeah

Answer 15

wait im doing it right now

Answer 16

ok

Answer 17

so whats the volume of the cone and the cylinder

Answer 18

@prowrestler .. u just read my comments... n it would be clear to u (i guess)

Answer 19

i gotcha

Answer 20

im confused so whats the radius and the height i need to know them to plug it into the formuas

Answer 21

first of all see the diagram that i had drawn..

Answer 22

and fan me guys

Answer 23

yes i see it

Answer 24

so can u see that clearly the height of the cylinder and cone is equal..and so is the radius

(its because cos, the question says that the cone "exactly" fits into the cylinder)

Answer 25

sp what is it

Answer 26

*so

Answer 27

since Volume of cylinder = pi r^2 h
Volume of cone = 1/3 pi r^2 h

and radius and height are equal for both so u can find out the value of volume of cone using
\[volume of cone = \frac{ 1 }{ 3 } \pi r ^{2} h\]

Answer 28

and u know that here \[\pi r ^{2} h\] = 81

Answer 29

oh ok

Answer 30

thats the radius right

Answer 31

so is it clear now ??

Answer 32

n BTW which grade r u in?

Answer 33

im 11th

Answer 34

ok..

Answer 35

so whats the height for them both

Answer 36

thats same i guess it could be clear from the diagram i made..
and when it comes to radius.
since u can see that they share.the common circular end..
so since the circumference is same therefore as a result the radius is also same...

Answer 37

so thats the answer @gudden

Answer 38

27 cubic feet would come out to be ur final answer..

Answer 39

Thnks man!!

Answer 40

i m a gal...xd,..

Answer 41

oh sorry:)

Answer 42

its alright...:D