A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.8 cm (see Fig. 13.11). Find its (i) inner curved surface area, (ii) outer curved surface area, (iii) total surface area
Answers
Answer:
1 inner curved surface area
According to the question inner diameter is 4 cm,
then,
Inner radius of a cylindrical pipe =r
1
=
2
inner diameter
=(24 )cm=2cm
Height (h) of cylindrical pipe=77 cm,
Curved Surface Area of inner surface of pipe =2πr
1 h
=(2×
7
22
×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
=
2
outerdiamterer
=(
2
4.4
)cm=2.2cm
Height of cylinder = h = 77 cm,
Curved area of outer surface of pipe = 2πr
2
h
=(2×
7
22
×2.2×77)cm
2
=(2×22×2.2×11)cm
2
=1064.8cm
2
iii)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
=πr
2
2
−πr
1
2
=
7
22
×((2.2)
2
−(2)
2
)
=
7
22
×(4.84−4)
=
7
22
×(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
Step-by-step explanation: