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
(1) inner curved surface area,
(ii) outer curved surface area,
(ii) total surface area.​

Answer 1

Answer:

(i) inner curved surface area

According to the question inner diameter is 4 cm,

then,

Inner radius of a cylindrical pipe =r

inner diameter/2 =(4/2)cm = 2 cm

Height (h) of cylindrical pipe=77 cm,

Curved Surface Area of inner surface of pipe =2πr1h

=(2× 22/7×2×77)cm²

=968cm²

(ii) Outer curved surface area

According to the question outer diameter is 4.4 cm

Outer radius of cylindrical pipe =r2 =

outer diameter/2 =(4.4/2)cm= 2.2cm

Height of cylinder = h = 77 cm,

Curved area of outer surface of pipe = 2πr2h

=(2×22/7 ×2.2×77)cm²

=(2×22×2.2×11)cm²

=1064.8cm²

(iii) Total surface area

Total surface area = curved surface area of inner cylinder + curved surface of outer cylinder + 2 × Area of base

Area of base = area of circle with radius 2.2 cm - Area of circle with radius 2 cm

=πr2² −πr1²

= 22/7 ×[(2.2)² - (2)²]

= 22/7 ×(4.84−4)

= 22/7 ×(0.84)

=2.74cm²

Total surface area = curved surface area of inner cylinder + curved surface area of outer cylinder + 2 × Area of base

=968+1064.8+2×2.74

= 2032.8 + 5.76

=2039.08cm²

Therefore, the total surface area of the cylindrical pipe is

=2039.08cm²

Step-by-step explanation:

I hope it's help to you