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

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

(i) Radius(r)= 2cm

Therefore volume=\(\frac{4}{3}\pi r^{3}\)

=\(\frac{4}{3}\times\frac{22}{7}\times\left ( 2 \right )^{3}\)

=33.52\(cm^{3}\)

(ii) Radius(r)= 3.5cm

Therefore volume=\(\frac{4}{3}\pi r^{3}\)

=\(\frac{4}{3}\times\frac{22}{7}\times\left ( 3.5 \right )^{3}\) = 179.666\(cm^{3}\)

(iii) Radius(r)= 10.5cm

Therefore volume=\(\frac{4}{3}\pi r^{3}\)

=\(\frac{4}{3}\times\frac{22}{7}\times\left ( 10.5 \right )^{3}\) = 4851\(cm^{3}\)