From a solid sphere if a diameter 6cm one hollow right circular cylinder has been made if length of a cylinder is 4cm and outer radius is 10cm find its inner radius .
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Step-by-step explanation:
Let inner radius of the cylinder be x cm
Given that radius of sphere =6cm
∴ Volume of the sphere =
3
4
π(r
′
)
3
=
3
4
×π×(6)
3
=4×π×2×36 cm
3
It is also given that external radius of base of cylineder (R)=5cm
and height =32cm
∴ Volume of hollow cylinder =πh[R
2
−r
2
]
=π×32×[(5)
2
−x
2
]
=32π[25−x
2
]
Solid sphere is melted and casted into hollow cylinder
∴ Volume of sphere = Volume of hollow cylinder
⇒ 4×π×2×36=32π[25−x
2
]
⇒
32
8×36
=25−x
2
⇒ 9−25=−x
2
⇒ x
2
=16
⇒ x=±4
⇒ x=4cm
Hence, the inner radius of the cylinder is 4cm
So, the thickness of the cylinder = external radius - inner radius
=5−4
=1cm
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