Question

helpp

A cylinder has its height doubled and its radius cut to one third. What is the ratio of the volumes of the modified cylinder to the original cylinder?

Answer 1

doubling the height doubles the volume
if the RADIUS is reduced to 1/3 its size, the volume is reduced by 1/9
so the volume is changed by 2/1 * 1/9 equals
2/9 of the original.

Answer 2

is there a formula ?

Answer 3

@DDCamp can you please help me?

Answer 4

The volume of a cylinder is:
\[V_{1} =h \pi r^{2}\]

If you double the height (h ---> 2h)
You get

\[V_{2} = 2h \pi r^{2}\]

Which is the double of V1.

If you cut the radius to a third (r ----> r/3 )

You get
\[V_{3} = 2h \pi \left( \frac{ r }{ 3 } \right)^{2} = \frac{ 2 }{ 9 } h \pi r^{2}\]

Answer 5

So the Volume is transformed to 2/9ths the original volume (V1).

Answer 6

Thanks Lessis :)

Answer 7

No problem. ;D