The internal and external radii of a hollow sphere are 3 cm and 5 cm respectively. The sphere is melted to from a solid cylinder of height `2""2/3cm`. Find the diameter and the curved surface area of the cylinder.

Answer

`11713cm^(2)`

Explanation

External radius of the sphere,` r_(1)=5 cm`.
Internal radius of the sphere, `r_(2)=3 cm `.
Volume of metal in the hollow sphere
`=4/3pi(r_(1)^(3)-r_(1)^(3))=[4/3pixx(5^(3)-3^(3))]cm^(3)`
`=((329pi)/3)cm^(3)`
Let the radius of the solid cylinder be R cm.
Height of the cylinder, `h=8/3 cm.`
Volume of the solid cylinder
`=piR^(2)h(piR^(2)xx8/3)cm^(3)=((8piR^(2))/3)cm^(3).`
Volume of cylinder = volume of metal in the hollow sphere
`rArr" "(8piR^(2))/3=(392pi)/3rArrR^(3)=49rArrR=7`.
`:." diameter of the cylinder formed "=(2xx7) cm = 14 cm`.
Curved surface area of the cylinder
`=2pirh=(2xx22/7xx7xx8/3)cm^(2)`
`=(352)/3cm^(2)=11713cm^(2)`.