# 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

h  =  14 cm

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   {R  -    r}           =   176

14 *  22/ 7  {R  -    r}    =   176

44  {R  -    r}    =   176

{R  -    r}        =   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
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