Question

An iron pipe 20 cm long has exterior diameter equal to 25 cm.if the thickness of the pipe is 1 cm,find the whole surface area of the pipe.

Answer 1

Solution:-

Height of pipe = 20 cm
External diameter = 25 cm 
External radius = 25/2 = 12.5 cm
Internal diameter = 25 - (1 + 1)
= 23 cm
Internal radius = 23/2 = 11.5 cm

Let the external radius be R and the internal radius be r.
Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)
⇒ 2*22/7*20(12.5 + 11.5) + 2*22/7*{(12.5)² - (11.5²)
⇒ (44*480)/7 + (44*24)/7
⇒ 21120/7 + 1056/7
⇒ 22176/7
= 3168 cm²
So, the total surface area of the pipe is 3168 square cm.

Answer 2

Height of pipe = 20 cm

External diameter = 25 cm  

External radius = 25/2 = 12.5 cm

Internal diameter = 25 - (1 + 1)

= 23 cm

Internal radius = 23/2 = 11.5 cm

Let the external radius be R and the internal radius be r.

Total surface area of the pipe = 2πh(R + r) + 2π(R² - r²)

⇒ 2*22/7*20(12.5 + 11.5) + 2*22/7*{(12.5)² - (11.5²)

⇒ (44*480)/7 + (44*24)/7

⇒ 21120/7 + 1056/7

⇒ 22176/7

= 3168 cm²

hope it will help