circular cylinder 14 cm long is 88 CM square if the volume of metal used in making the cylinder is 176 cm cube find the outer and inner diameter of cylinder
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Answer:
Outer radius = 5/2
Inner radius = 3/2
Step-by-step explanation:
Given,
Height of the hollow cylinder = h = 14 cm
According to question,
Outer curved surface area of cylinder - Inner curved surface area of cylinder = 88
Applying the formula ,
2 π h ( R - r ) = 88 where R is the outer radius and r is inner radius
Taking π = 22/7
2 * ( 22/7 ) * 14 * ( R - r ) = 88
R - r = 1 [ Let this be Eqn 1 ]
Also given,
Volume of outer part - Volume of inner part = 176
Applying the formula ,
π h ( R² - r² ) = 176
π h ( R + r ) ( R - r ) = 176
Substituting the value of ( R - r ) = 1 from Eqn 1,
π h ( R + r ) ( 1 ) = 176
π h ( R + r ) = 176
Substituting the value of π and h ,
( 22/7 ) * 14* ( R + r ) = 176
R + r = 4 [ Let this be Eqn 2 ]
Adding Eqn 1 and Eqn 2,
R - r + R + r = 4 + 1
2R = 5
R = 5/2
Substituting value of R in Eqn 1,
5/2 - r = 1
r = 5/2 - 1
r = 3/2
Hence,
Outer radius = 5/2
Inner radius = 3/2