Question

Find the total surface area of an open pipe of length 50 cm, external diameter 20 cm and internal diameter 6 cm.

Answer 1

Length of an open pipe = 50 cm 

External diameter = 20 cm ${\displaystyle \Rightarrow }$ External radius (R) = 10 cm 

Internal diameter = 6 cm ${\displaystyle \Rightarrow }$ Internal radius (r) = 3 cm 

Surface area of pipe open from both sides = 2πRh + 2πrh

= 2πh(R + r)

= ${\displaystyle 2\times \frac{22}{7}\times 50\times (10+3)}$

= 4085.71 cm²

Area of upper and lower part = 2π(R² – r²)

= ${\displaystyle 2\times \frac{22}{7}\times ({10}^2-3^2)}$

= ${\displaystyle 2\times \frac{22}{7}\times (100-9)}$

= ${\displaystyle 2\times \frac{22}{7}\times 91}$ 

= 572 cm²

Total surface area = 4085.714 + 572

= 4657.71 cm²