The difference between outer and inner curved surface area of a hollow right circular cylinder is 14...........

Quantitative Aptitude ( CCS) Mensuration 3D

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

1 cm

2 cm

3 cm

2.5 cm

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Explanation:

Given,
Height of the hollow cylinder = 14 cm
Let the internal and external diameters of the hollow cylinder be r and R respectively.
Given that the difference between inner and outer curved surface =88 cm3
Curved surface area of a hollow cylinder = 2∏(R−r)×h
88=2π(R-r)* h
88=2*3.1428*(R-r)*14
R-r =1 …………………………..(i)
Volume of the hollow cylinder = ∏(R²−r²)×h
Volume of the hollow cylinder= 176cm³
π (R²-r²) h =176
R²-r² = 4
R+ r = 4 …………………………..(ii)
Now, solving eq I and ii we get,
R-r = 1
R+ r = 4
………………………………..
2R = 5
R=2.5 cm
r = 1.5 cm
The internal and external radii of the hollow cylinder are 1.5 cm and 2.5 cm respectively.