The difference between the outer and inner curved surface areas of a hollow right circular cylinder ...........

Quantitative Aptitude ( CCS) Mensuration 3D

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

3 cm

5 cm

7 cm

9 cm

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Explanation:

Given,
Height of the cylinder = 14 cm
Let the inner and outer radii of the hollow sphere be (r) and (R) respectively.
The difference between inner and outer curved surface area is 88 cm 2
Curved surface area of the hollow sphere = 2π(R-r) h
88 = 2π(R-r) h
88 = 2π(R-r) 14
R-r = 1 ………………………………….. (i)
Volume of the hollow cylinder = ∏×R²−r²×h
176 = ∏×R²−r²×h
176 = ∏×R²−r²×15
From equation (i) substituting the values of equation. We get,
R+ r = 4……………………………………. (ii)
Now solving both the equations we get,
2R= 5
R= 2.5cm & r = 1.5 cm
Inner radius of the hollow cylinder = 1.5 cm
Inner diameter of the hollow cylinder = 2 * 1.5 cm = 3 cm
Outer radius of the hollow cylinder = 2.5 cm
Outer diameter of the hollow cylinder = 5 cm