Question

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 . ​

Answer 1

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