Question

a metal pipe is 77 cm long, the inner diameter of the cross- section is 4 cm and the outer diameter is 4.4cm. find the 1. inner curved surface area2. outer curved surface area3. total surface area​

Answer 1

(i) inner curved surface area

According to the question in ner diameter is 4 cm,then,In ner radius of a cylindrical pipe =r 1

= inner diameter/2

=( 4/2 )cm=2cm

Height (h) of cylindrical pipe=77 cm,

Curved Surface Area of inner surface of pipe =2πr 1 h

=(2× 22/7 ×2×77)cm^2

=968cm^2

(ii) Outer curved surface area

According to the question outer diameter is 4.4 cm

Outer radius of cylindrical pipe =r^2

= outer diamterer/2

=( 4.4/2 )cm=2.2cm

Height of cylinder = h = 77 cm,

Curved area of outer surface of pipe =2πr^2h

=(2×22/7×2.2×77)cm^2

=(2×22×2.2×11)cm^2

=1064.8cm^2

(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

=πr2^2−πr1^2

= 22/7 ×((2.2)^2−(2)^2)

= 22/7×(4.84−4)

= 22/7×(0.84)

=2.74cm^2

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

=2039.08cm ^2

Therefore, the total surface area of the cylindrical pipe is

=2039.08cm ^2

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