Q9 of 44 Page 14

A solid sphere of radius 6cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 5cm and its height is 32 cm, find the uniform thickness of the cylinder.

Let inner radius of the cylinder be x cm


Given that radius of sphere = 6cm



=


= 4 × π × 2 × 36 cm3


It is also given that external radius of base of cylinder (R) = 5cm


and height = 32cm


∴ Volume of hollow cylinder = πh[R2 – r2]


= π × 32 × [(5)2 – x2]


= 32π [25 – x2]


Solid sphere is melted and casted into hollow cylinder


∴ Volume of sphere = Volume of hollow cylinder


⇒ 4 × π × 2 × 36 = 32π [25 – x2]



⇒ 9 – 25 = -x2


⇒ x2 = 16


⇒ x = ±4


⇒ x = 4cm


Hence, the inner radius of the cylinder is 4cm


So, the thickness of the cylinder = external radius – inner radius


= 5 – 4


= 1cm


More from this chapter

All 44 →
7

Spherical ball of diameter 21cm is melted and recasted into cubes, each of side 1 cm. Find the number of cubes thus formed. [Use π=22/7]

 8

The internal and external diameters of a hollow hemispherical shell are 6cm and 10cm respectively. It is melted and recast into a solid cone of base diameter 14cm. Find the height of the cone so formed.

 10

The diameter of a copper sphere is 6cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 36cm, find its radius [Take π=2.14]

 11

A cylindrical container is filled with ice-cream. Its diameter is 12cm and height is 15cm. The whole ice-cream is distributed among 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream cone.