Question

An iron pipe $20$cm long has external radius equal to $12.5$cm and internal radius equal to $11.5$cm. Find the total surface area of the pipe.

Answer 1

Given: Length of pipe $\left(h\right)=20cm$

External radius of pipe $\left(R\right)=12.5$ cm

Internal radius of pipe $\left(r\right)=10.5$ cm

Now,

Total Surface area (TSA) of pipe $=$ Internal Curved Surface area of pipe +External curved surface area of pipe +Area of Concentric base of the pipe

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

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

$=2\pi \times 20(12.5+11.5)+2\pi (12.5+11.5)(12.5-11.5)$

$=2\pi (12.5+11.5)(20+1)$

$=2\times \frac{22}{7}\times 24\times 21$

$=3168c{m}^2$