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Which of the subsequent is not correct for a hollow cylinder?

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Curved surface area

= 2 π h (R + r)

Total surface area

= 2 π (R + r) (h + R − r)

Inner curved surface area

= 2 π h (R − r)

Area of each end

= π R 2 − r 2

answer is C.

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Detailed Solution

We have given a hollow cylinder.
We know that the curved surface area of a cylinder is

2 π r h,

where r is the radius of the base and h is the cylinder's height.
Construct a hollow cylinder with inner radius r and outer radius R.
Question Image

For a hollow cylinder,
The inner curved surface area is

2 π r h .

The curved surface area is

2 π h R + r .

The total surface area is

2 π R + r h + R − r .

Calculate the area of each end as shown:

External area − internal area = π R 2 − π r 2 = π R 2 − r 2

The area of each end is

π R 2 − r 2 .

Since, the inner curved surface area of a hollow cylinder is

2 π r h,

therefore, option (3) is correct.

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