Question

the volume of a solid metal Bob of radius 6 cm is dash​

Answer 1

Explanation:

Given,

The diameter of solid metal sphere D=6 cm

Hence, radius of solid metal sphere r=

2

D

=3 cm

The solid sphere is melted and a circular disk of thickness h=1 cm is prepared.

Let the radius of the circular disk be R cm

Given that the solid sphere is melted and form a circular disk.

→ Volume of circular disk = Volume of solid sphere .

→πR

2

h=

3

4

πr

3

→R

2

=

3h

4r

3

→R

2

=

3×1 cm

4×3

3

cm

3

→R

2

=4×3

2

cm

2

→R

2

=4×9 cm

2

→R

2

=36 cm

2

→R=6 cm

Hence the diameter of the circular disk d=2×R=12 cm

Answer 2

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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