Login

The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14cm long, is 88cm2. If the volune of metal used in making the cylinder is 176cm3, find the outer and inner diameters of the cylinder

We have to find the inner and the outer radius of a hollow cylinder whose height(h) = 14 cm

So,

Outer curved surface area - Inner curved surface area = 88

 .......(1)

Also we have,

Volume of outer part - Volume of inner part = 176

.......(2)

Using (1) and (2), we get,

  • 101
View Full Answer

  h  =  14 cm  

let external radius and inner radius be R  and  r  respectively.

    outer surface  -  inner surface  =   88

        2pie R h  -  2pie r h    =  88

       2* h pie  {R - r}   =   88

     2 * 14 * 22/7 {R  - r}   =   88           =>     88   {R  - r}    =   88

      R   -   r    =1              ................1

           Voume of whole solid {R}   -   volume  of cylinder {r}     =   176

                   pie R2 h    -    pie r2 h            =   176

                  pie h   {R2   -    r2 }           =   176

                   14 *  22/ 7  {R2   -    r2 }    =   176

                      44  {R2   -    r2 }    =   176

                               {R2   -    r2 }        =   4

               {R  -  r} {R    +   r}    =    4

                     {1} {R    +   r}      =  4

                       {R    +   r}     =    4      ..............2

from   1 and  2

R    =  5/2           r   =   3 /2

external diameter  =   5 cm         and          inner diameter      =        3 cm

 

 

 

 

 

 

 

 

 

         

  • 31

 Let  the outer and inner diameter be R and r respectively

Difference between outer and inner CSA = 2*pi*R*h - 2*pi*r*h

= 2*pi*h*(R-r)

= 2*(22/7)*14*(R-r)

= 88 (given)

(R-r) =  88*7/(14*2*22)=1  ....... (1)

Volume of the hollow cylinder = pi * (R2-r2)*h = 22/7 *(R+r)*(R-r)*14

= 22/7*(R+r)*1*14

= 44(R+r)

= 176 (given)

R+r = 176/44 = 4 ........ (2)

(1)+(2) => 2R = 5 => outer diameter = 5 cm      (diameter =  2 * radius)

(1)-(2) => 2r =3 => inner diameter = 3 cm

  • 9
What are you looking for?