la cylinder and come have bases of equal radii and equal heights show that there volumes are in the ratio of 3:4
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Answer
For cylinder, we have
base radius=r, height=h
∴S
1
=Curved surface=2πrh
For cone, we have
l=
r
2
+h
2
and, S
2
=πrl=πr
r
2
+h
2
We have,
S
2
S
1
=
5
8
⇒
πr
r
2
+h
2
2πrh
=
5
8
⇒
r
2
+h
2
2h
=
5
8
⇒
r
2
+h
2
4h
2
=
25
64
⇒25h
2
=16r
2
+16h
2
⇒9h
2
=16r
2
⇒3h=4r
⇒
h
r
=
4
3
.
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