Question

The total surface area of an open pipe of length $50$ cm, external diameter $20$ cm and internal diameter $6$ cm is approximately

• A. $2787.84{cm}^2$
• B. $4655.84{cm}^2$
• C. $8693.84{cm}^2$
• D. $5742.84{cm}^2$

Answer 1

The correct option is B $4655.84{cm}^2$

Given, a pipe with inner diameter $6$ cm, outer diameter $20$ cm, length $50$ cm.
Inner diameter $=6$ cm, inner radius $=3$ cm
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 remaining circular portion
$=2\pi rh+2\pi Rh+2\pi (R^2-r^2)=2\times \pi \times 3\times 50+2\times \pi \times 10\times 50+2\times \pi \times 91=1482\pi {cm}^2=4655.84{cm}^2$