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

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

Height of the open pipe, $h=50cm$

External diameter $=20cm$

External radius, $R=10cm$

Internal diameter $=6cm$

Internal radius, $r=3cm$

An open pipe is a hollow cylider.

Total surface area of a hollow cylinder= External curved surface area + Internal curved surface area + 2(area of base rings)

$=2\pi Rh+2\pi rh+2\pi (R^2-r^2)$

$=2\pi h(R+r)+2\pi (R+r)(R-r)$

​$=2\pi (R+r)(h+R-r)$

$=2\times \frac{22}{7}(10+3)(50+10-3)c{m}^2$

$=2\times \frac{22}{7}\times 13\times 57=\frac{32604}{7}=4657.71c{m}^2$

Hence, total surface area of hollow cylinder is $4657.71c{m}^2$