Question

A metal pipe is $77$cm long. The inner diameter of a cross section is $4$cm, the outer diameter being $4.4$cm. Find its
(i) Inner curved surface area,
(ii) Outer curved surface area,
(iii) Total surface area.

Answer 1

Given,

Inner diameter(d)$=4$cm

$\Rightarrow$ Inner Radius (r) = $\frac{4}{2}=2$cm

Outer diameter(D)$=4.4$cm

$\Rightarrow$ Outer Radius (R) = $\frac{4.4}{2}=2.2$cm

Length of metal pipe$=77$cm

Now, surface area of a cylinder $=2\pi rh$ sq.cm, where,

$\pi =\frac{22}{7}$, $r=2$cm, $h=77$cm

$\therefore$ Inner curved surface area$=2\times \frac{22}{7}\times 2\times 77$

$=44\times 22$ sq. cm

$=968$ sq. cm

$\therefore$ Inner curved surface area($s_1$)$=968$ sq.cm

Surface area of outer sphere$=2\pi Rh$ sq.cm, where,

$\pi =\frac{22}{7}$, $R=2.2$cm, $h=77$cm

$\therefore$ Outer curved surface area$=2\times \frac{22}{7}\times 2.2\times 77$ sq.cm

$=22\times 2\times 2.2\times 11$ sq.cm

$=44\times 2.2\times 11$ sq.cm

$=1064.8$ sq.cm

$\therefore$ Outer curved surface area($s_2$)$=1064.8$ sq. cm

Now let us find total surface area as, we know that,

Total surface area $=$ Inner surface area $\left(s_1\right)+$Outer surface area $\left(s_2\right)$

T.S.A$=[968+1064.8]$ sq. cm

= $2,032.8$ sq.cm

$\therefore$ Total surface area(s)$=2032.8$ sq.cm