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# The Diameters of the Internal and External Surfaces of a Hollow Spherical Shell Are 6 Cm and 10 Cm Respectively. If It is Melted and Recast and Recast into a Solid Cylinder of Diameter 14 Cm, Find the Height of the Cylinder. - Mathematics

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#### Question

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

#### Solution

Internal diameter of hollow spherical shell = 6cm

Internal radius of hollow spherical shell =6/3=3 cm

External diameter of hollow spherical shell = 10 cm

External radius of hollow spherical shell = 10/2=5cm

Diameter of cylinder = 14 cm

Radius of cylinder=14/2=7cm

Let height of cylinder = xcm

According to the question

Volume of cylinder = Volume of spherical shell

⇒ pi(7)^2x xx=4/3pi(5^3-3^3)

⇒49x xx=4/3(125-27)

⇒49x xx=4/3xx98

x=(4xx98)/(3xx49)=8/3cm

∴Height off cylinder=8/3cm

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Ex. 14.1 | Q: 24 | Page no. 29
Solution The Diameters of the Internal and External Surfaces of a Hollow Spherical Shell Are 6 Cm and 10 Cm Respectively. If It is Melted and Recast and Recast into a Solid Cylinder of Diameter 14 Cm, Find the Height of the Cylinder. Concept: Volume of a Combination of Solids.
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