If the diameter of the base remains constant, by what factor should the altitude be multiplied to produce a cone with twice volume as the original?

Question

anonymous · Answer

@amistre64

anonymous · Answer

1/2?

anonymous · Answer

how did you get it?

amistre64 · Answer

how do we determine the volume of a cone?

anonymous · Answer

V= 1/3 pi r^2 h

amistre64 · Answer

now multiply both sides by 2

anonymous · Answer

2V =2(1/3 pi r^2h)

amistre64 · Answer

notice that r doesnt change,  1/3 and pi dont change ... we only change the height

what did we alter?

amistre64 · Answer

2V = 1/3 pi r^2  2h

anonymous · Answer

you said that i will multiple the other side means:
2/3*2pi*2r^2*2h = 2V

amistre64 · Answer

no .... you cant make up your own math rules ....

2(ab)  does not equate to  2a2b

amistre64 · Answer

if a remains the same, then we must have altered b .. by 2

anonymous · Answer

what do you mean, 1/3 *pi*r^2 are a fixed value?

amistre64 · Answer

the formula for volume doesnt change does it?

anonymous · Answer

yup

anonymous · Answer

can you show me your solutions

amistre64 · Answer

if the formula is consistent for all cones ... then  V = 1/3 pi r^2 h  is for any size cone

since 1/3 and pi are constant for any size cone ... and we are told ...

i did show you, they are posted above

amistre64 · Answer

why do i bother posting this stuff if noone has the gumption to just scroll up to look at it ....

anonymous · Answer

i am looking

amistre64 · Answer

:)  thnx

anonymous · Answer

no one wants to answer my qs so im looking at others while i wait and this is intresting

anonymous · Answer

so that means that if we double the height, it doubles the volume?

amistre64 · Answer

V1 the original cone:  1/3  pi r^2 h1

V2 the scaled cone:  1/3 pi r^2 h2

V2 = 2V1


1/3 pi r^2 h2 = 2(1/3  pi r^2 h1)

factor out common factors

 h2 = 2 h1

anonymous · Answer

so the golden rule what you do to one side do to the other. and we are inding x witch is ether our voluem or the fraction we want

amistre64 · Answer

we double the height to double the volume

which is logically what we would do if this is a cylindar ... and a cone is just  1/3 the colume of its representative cylindar

anonymous · Answer

that make sense ...lol...you must do it earlier so that we can move on another problem

anonymous · Answer

ok the h thing makes sense because 2 x 1 right?(sorry if im bothering you