Question

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

Answer 1

Given:
Height of a hollow right circular cylinder (h)= 14 cm  
Difference between outer and inner closed surface area of a hollow right circular cylinder  = 88 cm²
Volume of metal used in making cylinder= 176 cm³

Let external radius and inner radius be R  and r.

Outer surface area  of Hollow Cylinder - inner surface Area of Hollow Cylinder =   88 cm²
2π R h  - 2π r h  = 88
2πh (R - r) =  88
2× (22/7) × 14 (R  - r) = 88
2 × 22 × 2 (R - r)    
88 (R  - r) = 88
R  - r  = 88/88 =
R - r = 1.........................(1)

Volume of Hollow  Cylinder = π(R² - r² )h
176 = 22/7(R² - r² ) ×14
14× 22/ 7 {R²  - r² } = 176
44  {R² -  r² } = 176
{R² -  r² } = 176/44
{R² - r²}   = 4
{R - r} {R  + r} = 4

[a² - b² = (a+b)(a -b)]
(1){R    + r} = 4  [ from eq 1]

{R + r}  = 4 …... ....................(2)

R - r = 1
R + r  = 4   [ On Adding eq 1 & 2]
-----------------
2R = 5
R=  5/2       

External Radius of hollow cylinder(R) = 5/2

On Putting the value of R in eq 1.
R - r = 1
5/2 - r = 1
5/2 -1 = r
(5 -2)/2 = r
r = 3/2

Internal Radius of hollow cylinder(R) = 3/2

EXTERNAL DIAMETER of hollow cylinder  = radius /2 = (5/2) /2 = 5 cm

INNER DIAMETER of hollow cylinder = radius /2 = (3/2)/2  = 3 cm
Hence , the External & internal diameter of hollow cylinder = 5 cm & 3 cm.

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