The difference between the outer and the inner curved surfaces of a cylinder 14cm long is 88cm². Find the outer and the inner radii of the cylinder, given that the volume of the metal is 176cm³.
Answers
Step-by-step explanation:
Hint: The difference between the outer and inner curved surface area of hollow right circular cylinder 14cm long is 88cm2, using this we make our equation number one. Similarly, the difference of volume of inner and outer part of hollow right circular cylinder is also given, using this we make another equation named as equation number two. By adding both the equations, we get one of the diameters and putting the value of one of the diameters, we also get the value of another diameter.
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The difference of outer curved surface area and inner curved surface area is 88cm2 given in the question.
So,
Outer curved surface area – Inner curved surface area =88cm2.
Since, the curved surface area of a cylinder is
2 πrh, where r is the radius and h is the height of the cylinder.
In our problem, the height of the cylinder is 14 cm.
2 πRh − 2πrh = 882 πh(R−r)= 88R−r= 882×227×14R−r = 88×72×22×14R−r = 1.. (1) equatin
Also, the difference of volume of outer part and inner part of cylinder is given.
So, Volume of outer part – Volume of inner part=176.
Since, the volume of a cylinder is Pir2h, where r is the radius and h is the height of the cylinder.
PiR2h - πr2h = 176Pih(R2−r2) = 176
We expand the (R2−r2) using the identity (a2−b2) = (a−b)(a+b).
Pih (R−r)(R+r) = 176Pi × 14(R+r)= 176R+r = 176× 722× 14R+r = 4...(2)
Adding equation (1) and equation (2), we get
R+r+R−r=5
2 R = 5
R=5/2
D=5
Putting in equation (2),
5/2+r=4
r = 4−5/2
r = (8−5)/2
r=3/2
d=3.
Hence, the diameter of outer cylinder is 5cm and the diameter of inner cylinder is 3cm
