Question

3. A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter being 4.4 cm
(see Fig. 13.11). Find its
inner curved surface area,
a outer curved surface area,
(ie total surface area.
Fig. 13.11​

Answer 1

Answer:

Inner curved surface area = 968 cm²

Outer curved surface area = 1064.8 cm²

Total Surface area = 2038.08 cm²

Step-by-step explanation:

Inner curved Surface area: The inner circumference of the pipe=2πr =2×(22/7)×2=12.57 cm.

(Given that 4 cm is the inner diameter i.e. inner radius = 2 cm)

Hence, the inner curved area = (2πr)L=12.57×77=968 cm²

( Also that the length of the pipe is 77 cm)

Outer curved surface area: The outer circumference of the pipe=2πR

=2×(22/7)×2.2=13.828 cm.

(4.4 cm is the outer diameter i.e. outer radius = 2.2 cm)

Hence, the outer curved area = (2πR)L=13.828×77=1064.8 cm²

(The length of the pipe is 77 cm)

Total Surface Area of the pipe:  The TSA of the pipe is given by

(2πr)L+(2πR)L+2π(R²-r²) (Since, the side surface area on one side is π(R²-r²)

= 968+1064.8+2(22/7)(2.2²-2²)

=2032.8 + 5.28

= 2038.08 cm²

Answer 2

Answer:

$2038.08\: \: {cm}^{2}$

Step-by-step explanation:

See the diagram to visualize problem

Curved Inner surface area

Inner surface has length of 77 cm and diameter of

4 cm or radius of 2 cm

So area

$= 2\pi \: rh = 2 \times \frac{22}{7} \times2 \times 77 = 968 \: {cm}^{2}$

Curved outer surface area

Inner surface has length of 77 cm and diameter of

4.4 cm or radius of 2.2 cm

So area

$= 2\pi \: rh = 2 \times \frac{22}{7} \times 2.2 \times 77 = 1064.8 \: {cm}^{2}$

Total surface area

Now we only have to calculate side area ( see figure ) which is difference of two circles .

$=2( \pi {(2.2)}^{2} - \pi {(2)}^{2}) = 2×\frac{22}{7} \times 0.84 = 5.28{cm}^{2}$

So total area

$968 + 1064.8 \: + 2.64 \: = 2038.08 \: {cm}^{2}$