the diameter of two cylinders are in the ratio of 2 ratio 3 find the ratio of their height is their volume are equal
Answers
Answer:
Step-by-step explanation:Let the ratio of height of two cylinders be
k
:
1
, say heights are
k
h
and
h
As diameters are in the ratio of
2
:
3
, let diameters be
2
d
and
3
d
.
Hence their volumes are
π
(
2
d
2
)
2
×
k
h
=
π
k
h
d
2
and
π
(
3
d
2
)
2
×
h
=
9
π
4
h
d
2
As two volumes are equal, we have
π
k
h
d
2
=
9
π
4
h
d
2
or
k
=
9
π
4
h
d
2
π
h
d
2
=
9
:
4
Hence ratio of their heights is
9
:
4
Answer:
The ratio of the diameters of the cylinders = 3 : 2
The ratio of the radius of the cylinders will be = 3 : 2
Therefore, let the radii of the two cylinder be 3x and 2x respectively.
Let the height of the cylinder be h1 and h2.
Now, Volume of first cylinder = Volume of the second cylinder
i.e., π(3x)²h1 = π(2x)²h2
h1/h2 = (π*4x²)/(π*9x²)
h1/h2 = 4/9
h1 : h2 = 4 :9
So, ratio of their heights is 4 : 9
please mark as brainliest