Question

The internal and external radii of a hollow sphere are 3cm and 5cm .the sphere is melted to form a cylinder of height 22/3 cm.find C.S.A of cylinder

Answer 1

Step-by-step explanation:

Volume of the material of hollow sphere = (4/3)π ×(R³ - r³)

                                                                = (4/3)π×(5³ -3³)                                                                                                                     = 392π/3 cm³

now it is melted to form cylinder ,

so volume of cylinder = volume of the material of sphere

⇒π r² ×h =392π/3 cm³

⇒r² = (392×3)/( 32×3)

     = 12.25

⇒r =√12.25 = 3.5 cm

so diameter of cylinder = 3.5×2 = 7 cm

Answer 2

Volume of hollow sphere = 4/3 pie ( 5^3 - 3^3)

= 4/3 pie ( 125 -27)

= 4/3 pie ( 98)

volume of cylinder = pie r^2 h

= pie r^2 22/3

Volume of sphere= volume of cylinder

4/3 pie (98) = pie r^2 × 22/3

4/3 × 98 = r^2 × 22/3

4× 98/ 22 = r^2

17.8 = r^2

r= 4.219

CSA of cylinder = 2 pie r h

= 2 × 3.14 × 4.219 × 22/3

= 194.29 cm^2