a cylinder and a cone have equal radius of their curved surface area are in the ratio 8:5 so that there radius and height of each has ratio 3:4
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Consider the curved surface area of cylinder and cone as 8x and 5x
So we get
2π rh=8x....(1)
πr
(h
2
+r
2
)
=5x.....(2)
By squaring equation (1)
(2πrh)
2
=(8x)
2
So we get
4π
2
r
2
h
2
=64x
2
....(3)
By squaring equation (2)
π
2
r
2
(h
2
+r
2
)=25x
2
.....(4)
Dividing equation (3) by (4)
π
2
r
2
(h
2
+r
2
)
4π
2
r
2
h
2
=
25x
2
64 x
2
On further calculation
(h
2
+r
2
)
h
2
=
25
16
It can be written as
9h
2
=16r
2
So we get
h
2
r
2
=
16
8
By taking square root
h
r
=
4
3
We get
r:h=3:4
Therefore, it is proved that the radius and height of each has the ration 3:4
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