Question

solid sphere of radius is melted into cylinder of height 9 cm base radius of cylinder

Answer 1

Step-by-step explanation:

Given,

Radius of solid sphere is r

Hight of hollow cylinder h=24 cm

External radius of base of cylinder R

2

=4 cm

Thickness of hollow cylinder t=2 cm

Hence, inner radius of the hollow cylinder = External radius(R) - thickness of cylinder (t)

Inner radius R

1

=(4−2) cm=2 cm

Now,

Volume of solid sphere V=

3

4

πr

3

And, Volume of hollow cylinder V=πh(R

2

2

−R

1

2

)

solid sphere of radius rr is melted and recast into a hollow cylinder of uniform thickness.

→Volume of sphere = Volume of hollow cylinder

3

4

πr

3

=πh(R

2

2

−R

1

2

)

r

3

=

4π

3πh(R

2

2

−R

1

2

)

r

3

=

4

3h(R

2

2

−R

1

2

)

r

3

=

4

3×24×(4

2

−2

2

)

cm

3

r

3

=

4

3×24×(16−4)

cm

3

r

3

=

4

3×24×12

cm

3

r

3

=

4

864

cm

3

r

3

=216 cm

3

r

3

=(6)

3

cm

3

r=6 cm