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A metal pipe measures 63 cm long. It has a 4.4 cm outside diameter and a 4 cm interior diameter. Then which of the following is not correct?

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Its inner curved surface area

= 792 cm 2

Its outer curved surface area

= 871.2 cm 2

The surface area of each end =

2.64 cm 2

Total surface area

= 1655.84 cm 2

answer is D.

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Detailed Solution

Given, a metal pipe that measures 63cm long.
Its inner diameter

= 4 c m .

⇒ r 1 = 2 c m

Outer diameter

= 4.4 c m .

⇒ R 2 = 2.2 c m

Therefore the inner curved surface area can be calculated as,

S 1 = 2 π r 1 h ⇒ S 1 = 2 π (2) (63) ⇒ S 1 = 792 c m 2

The outer curved surface area of the metal pipe can be calculated as,

S 2 = 2 π R 2 h ⇒ S 2 = 2 π (2.2) (63) ⇒ S 2 = 871.2 c m 2

The surface area of each side of the metal pipe can be calculated as,

S 3 = π (R 22 − r 12) ⇒ S 3 = π (2.2) 2 − (2) 2 ⇒ S 3 = 2.64 c m 2

Now, the total surface area of a metal pipe can be calculated as,

S 4 = S 1 + S 2 + 2 S 3 ⇒ S 4 = 792 + 871.2 + {2 (2.64)} ⇒ S 4 = 1665.84 c m 2

Thus, the total surface area of the metal pipe is

1665.84 c m 2 .

Hence, option (4) is correct.

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