The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the total surface area of the pipe ( take \(\pi = \frac{22}{7}\) ) correct to two places of decimal.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 2)

Answer 1

Given:

The external diameter of an iron pipe is 20 cm and its length is 12 cm.

Its length is 12 cm and the thickness of the pipe is 1 cm.

Concept used:

1. Curved surface of a cylinder = 2πrh (where r = Radius of the base, h = height)

2. Total surface area of the pipe = Outside surface area + inside surface area + Top Base Area + bottom base area

3. Area of a circle = πR² (R = Radius)

Calculation:

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External radius of the iron pipe, R = 20/2 = 10 cm

Internal radius of the iron pipe, r = 10 - 1 = 9 cm

Height, h = 12 cm

According to the concept,

2πRh + 2πrh + π(R²−r²) + π(R²−r²)

⇒ 2πh(R + r) + 2π(R2−r2)

⇒ 2π {12 × (10 + 9) + (10² - 9²)}

⇒ 1552.5714 ≈ 1,552.57 cm2

∴ The total surface area of the pipe is 1,552.57 cm2.