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A hollow cylinder having external radius 8 cm and height 10 cm has a total surface area of $338 π cm 2$ . Find the thickness of the hollow metallic cylinder.

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2 cm

3 cm

4 cm

5 cm

answer is B.

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Detailed Solution

Given,
External radius 8 cm and height 10cm,
Total surface area

= 338 π c m 2

Let the internal radius of the hollow cylinder = r cm
Total surface area,

⇒ 2 π R + 2 π r + 2 π (R 2 − r 2) = 38 π

= 2 π (R h + r h + R 2 − r 2) = 338 π → (1)

⇒ (10 × 8) + (10 × r) + (8) 2 − r 2 = 338 π 2 π

⇒ (80) + (10 r) + 64 − r 2 = 169 ⇒ − r 2 + 10 r = 169 − 144 ⇒ − r 2 + 10 r = 25 → (2)

⇒ r 2 − 10 r + 25 = 0

⇒ r 2 − (5 + 5) r + 25 = 0 ⇒ r 2 − 5 r − 5 r + 25 = 0 ⇒ r (r − 5) − 5 (r − 5) = 0

⇒ (r − 5) = 0 ⇒ r = 5

Now as we know the thickness of a hollow cylinder can be obtained by subtracting the inner radius which is r from the outer radius which is R as given in the solution hint. Therefore
The thickness of the metal

When substituting the values in the above expression

⇒ 8 − 5 = 3 c m

Hence, option 2 is correct.

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