Question

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Answer 1

Height = 77 cm

Inner diameter = 4 cm

Outer diameter = 4.4 cm

Find the inner radius:

$\boxed {\text{Radius = Diameter}\div 2}$

Radius = 4 ÷ 2 = 2 cm

Find the outer radius:

$\boxed {\text{Radius = Diameter}\div 2}$

Radius = 4.4 ÷ 2 = 2.2 cm

Find the inner curved surface area:

$\boxed{ \text{Curved surface area =} 2\pi rh}}$

Curved surface area = 2 x 22/7 x 2 x 77 = 968 cm²

Find the outer curved surface area:

$\boxed{ \text{Curved surface area =} 2\pi rh}}$

Curved surface area = 2 x 22/7 x 2.2 x 77 = 1064.8 cm²

Find the surface area of the top and bottom:

$\text{Surface Area = }2( \pi r^2h - \pi r^2h )$

Surface area = 2[ 22/7 x 2.2² - 22/7 x 2² ]

Surface area = 5.28 cm²

Find the total surface area:

Total surface area = inner CSA + Outer CSA + Top and Bottom

Total surface area = 968 + 1064.8 + 5.28 = 2038.08  cm²

Answer: (1) 968 cm² (2) 1064.8 cm² (3) 2038.08  cm²

Answer 2

$\mathbb{ SOLUTION }$ :

Given :
height (h) of the hollow metal pipe = 77cm

Inner diameter = 4cm
Inner radius (r) = $\frac{4}{2}$ = 2cm

$\boxed{\boxed{ \therefore radius = \frac{diameter}{2} }}$

Outer diameter = 4.4cm
Outer radius (R) = $\frac{4.4}{2}$ = 2.2cm

$\boxed{\boxed{ \therefore radius = \frac{diameter}{2} }}$

Formula of Curved Surface Area (CSA) = 2πrh

,

(i) Inner Curved Surface Area,

= 2 × $\frac{22}{7}$ × 2 × 77 cm²

= $\boxed{\boxed{ 968 {cm}^{2} }}$

.

(ii) Outer Curved Surface Area,

= 2 × $\frac{22}{7}$ × 2.2 × 77 cm²

= $\boxed{\boxed{ 1064.8 {cm}^{2} }}$

,

(iii) Total Surface Area of hollow metallic pipe,

Formula : 2π (R+r)(h+R-r)

= 2 × $\frac{22}{7}$ (2.2 + 2) (77 + 2.2 - 2)

= $\frac{44}{7}$ × 4.2 × 77.2

= $\boxed{\boxed{ 2038.08 {cm}^{2} }}$