Important problem from the cbse board exam point of view; becuse last time this problem was asked in 2012. Problem from RS Aggarwal book, problem number 5, page number 809, exercise 17B, chapter volume and surface area of solid.
The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm, respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.
The internal base radius of spherical shell, r1 = 3 cm,
the external base radius of spherical shell, R = 5 cm
the base radius of solid cylinder, r = 14/2 = 7 cm
Volume of the spherical shell = Volume of the cylinder
[4/3] π [ R³ – r1³ ] = π r² h
[4/3] [ R³ – r1³ ] = r² h
[4/3] [ 5³ – 3³ ] = [ 7² ] * h
( [4/3] * 98 ) / 49 = h
∴ The height of the cylinder is 8/3cm