Question

The external diameter of a 20 CM long and 1cm thick hollow iron pipe is 25cm. Determine the whole surface of the iron pipe​

Answer 1

Answer:

Step-by-step explanation:

$\underline{\bold{Given:-}}$

Height of pipe = 20 cm

External Diameter = 25 cm

Radius = $\sf \frac{25}{2} =12.5 \: cm$

Internal Diameter = 25 - 2 = 23 cm

Radius = $\sf \frac{23}{2} =11.5 \: cm$

$\underline{\bold{To \: Find:-}}$

Total surface area of the pipe

$\underline{\bold{Formula \: to \: be \: used:-}}$

$\sf Total \: Surface \: Area = 2\pi h(R + r) + 2\pi (R^2 - r^2)$

$\underline{\bold{Solution:-}}$

Let the external radius be R.

And the internal radius be r.

Putting all the values, we get

$\sf\implies Total \: Surface \: Area = 2\pi h(R + r) + 2\pi (R^2 - r^2)$

$\sf\implies Total \: Surface \: Area =2\times\frac{22}{7}\times20\times(12.5 + 11.5)+2\times\frac{22}{7}\times[(12.5)^2 - (11.5)^2]$

$\sf\implies Total \: Surface \: Area =\frac{21120}{7}+\frac{1056}{7}$

$\sf\implies Total \: Surface \: Area =\frac{22176}{7}$

$\bf\implies Total \: Surface \: Area =3168 \: cm^2$

Hence, The whole surface of the iron pipe​ is 3168 cm²

Answer 2

AnswEr :

$\bold{Given} \begin{cases}\sf{Height(h)=20 \: cm} \\ \sf{External \: Diameter=25 \: cm} \\ \sf{External \: Radius(R)= \dfrac{25}{2} = 12.5 \: cm} \\ \sf{Internal \: Radius (r)=12.5 - 1 = 11.5 \: cm }\end{cases}$

• Now we will calculate TSA of Cylinder :

$\longrightarrow \sf 2\pi h(R + r) + 2\pi( {R}^{2} - {r}^{2} )$

$\longrightarrow \sf \bigg(2 \times \dfrac{22}{7} \times 20(12.5 + 11.5) \bigg) + \bigg(2 \times \dfrac{22}{7} \times ( {(12.5)}^{2} - {(11.5)}^{2} \bigg)$

$\longrightarrow \sf \bigg(2 \times \dfrac{22}{7} \times 20 \times 24 \bigg) + \bigg(2 \times \dfrac{22}{7} \times (12.5 + 11.5)(12.5- 11.5) \bigg)$

$\longrightarrow \sf \bigg(\dfrac{44 \times 480}{7} \bigg) + \bigg(\dfrac{44 \times 24}{7}\bigg)$

$\longrightarrow \sf \dfrac{44}{7} \bigg(480 + 24\bigg)$

$\longrightarrow \sf \dfrac{44}{ \cancel7} \times \cancel{504}$

$\longrightarrow \sf 44 \times 72$

$\longrightarrow \boxed{\large \sf 3168 \: cm^{2}}$

⠀

∴ WSA(TSA) of Cylinder is 3168 cm².