Question

find the total surface area of a cylindrical pipe of thickness 2 cm the external diameter of the pipe is 21 cm and its length is 3 m. ​

Answer 1

The total surface area of the cylindrical pipe is 596.6 square centimeter .

Step-by-step explanation:

Given as :

The thickness of the cylindrical pipe = t = 2 cm

The measure of external diameter of cylinder = D = 21 cm

The height of the cylinder = h = 3 m = 300 cm

Let The Total surface area of the cylindrical pipe = A square centimeter

According to question

∵ Total surface area of the cylindrical pipe = 2 × π × radius × height + 2 × π × radius²

i.e A = 2 × π × height (external radius + internal radius) + 2 × π × (external radius² - internal radius² ) ..........1

Now, Since The measure of external diameter of cylinder = D = 21 cm

So, The measure of external radius = R =

i.e R = cm

So, external radius = R = 10.5 cm

Again , ∵ Thickness of the cylindrical pipe = t = 2 cm

So Internal radius of the pipe = r = external radius - thickness

I.e r = R - t

Or, r = 10.5 cm - 2 cm

∴ r = 8.5 cm

So, internal radius = 8.5 cm

So, From equation 1 , we get

A = 2 × π × height (R + r) + 2 × π × (R² - r² )

Or, A = 2 × 3.14 × 3 (10.5 + 8.5) + 2 × 3.14 × (10.5² - 8.5² )

Or, A = 18.84 × (19) + 6.28 × (110.25 - 72.25)

Or, A = 357.96 cm² + 238.64 cm²

∴ Total surface area = 596.6 cm²

So, The total surface area of the cylindrical pipe = A = 596.6 cm²

Hence, The total surface area of the cylindrical pipe is 596.6 square centimeter . Answer

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