two circular cylinders of equal volumes have their height in ratio 1:2 ratio of their radio is...
Answers
Answer:
We know that the volume of a right circular cylinder with radius r and height h is V=πr
2
h.
It is given that the ratio of the heights of two circular cylinders is 1:2 that is
h
2
h
1
=
2
1
, therefore,
V
1
=V
2
⇒πr
1
2
h
1
=πr
2
2
h
2
⇒
r
2
2
r
1
2
=
h
1
h
2
⇒
r
2
2
r
1
2
=
h
2
h
1
1
⇒
r
2
2
r
1
2
=
2
1
1
⇒(
r
2
r
1
)
2
=2
⇒
r
2
r
1
=
2
Hence, the ratio of their radius is
2
:1.
Answer:
height ratio = 1:2
volume of first cylinder = πr²h
-------------------------------------------------
volume of second cylinder = πR²h
r²= vol. of first cylinder / πh
=> --------------------------------------------------
R²= vol. of second cylinder / π2h
r² 2 r √2
=>----- = ---- => ---- = ----- => √2:1
R² 1 R 1