What Length of a Solid Cylinder 2cm in Diameter Must Be Taken to Recast into a Hollow Cylinder of Length 16cm, External Diameter 20cm and Thickness 2.5mm? - Mathematics

What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow
cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?

Solution

Given that diameter of solid cylinder = 2cm

Given that solid cylinder is recast to hollow cylinder Length of hollow cylinder =16cm

External diameter = 20cm

Thickness = 2.5mm= 0.25cm

Volume of solid cylinder=pir^2h

So volume of solid cylinder=pi(1)^ 2h         ...........(i)

Let length of solid cylinder be h

Volume of hollow cylinder=pih(R^2-r^2)

Thickness =R - r

0.25 = 10 - r

So volume of hollow cylinder = π x 16(100 - 95.0625)                      .........(2)

Volume of solid cylinder is equal to volume of hollow cylinder.

(1)=(2)

Equating equations (1) and (2)

pi(1)^2h=pixx16(100-95.06)

22/7(1)^2xxh=22/7xx16(4.94)

h=79.04cm

∴Length of solid cylinder =79cm

Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 5 | Page 28