Question

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

• A. $4657.71$ $c{m}^2$
• B. $4677.71$ $c{m}^2$
• C. $4697.71$ $c{m}^2$
• D. $4717.71$ $c{m}^2$

Answer 1

The correct option is A $4657.71$ $c{m}^2$

Given, a pipe with inner diameter $6$ cm, outer diameter $20$ cm, length $50$ cm.
Inner diameter $=6$ cm, inner radius $=3$ cm $($ Diameter $=2$ $\times$ radius$)$
Outer diameter$=20$ cm, outer radius $=10$ cm
Total surface area of pipe $=$ Curved surface area of inner pipe $+$ curved surface area of outer pipe $+$ Area of top circular portion
$=2\pi rh+2\pi Rh+2\pi (R^2-r^2)=2\times \frac{22}{7}\times 3\times 50+2\times \frac{22}{7}\times 10\times 50+2\times \frac{22}{7}\times 91=942.85+3142.85+572=4657.7$