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Byju's Answer
Standard IX
Mathematics
Total surface area of a right circular cone
A right circu...
Question
A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio
8
:
5
, determine the ratio of the radius of the base to the height of either of them.
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Solution
C
S
A
o
f
c
y
l
i
n
d
e
r
C
S
A
o
f
c
o
n
e
=
8
5
⇒
2
π
r
h
π
r
l
=
8
5
⇒
h
l
=
4
5
⇒
5
h
=
4
l
⇒
5
h
=
4
√
h
2
+
r
2
Squaring both sides, we get
25
h
2
=
16
(
h
2
+
r
2
)
⇒
9
h
2
=
16
r
2
⇒
h
2
r
2
=
16
9
⇒
h
r
=
√
16
9
=
4
3
=
4
:
3
o
r
r
h
=
3
4
=
3
:
4
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