a metal pipe is 77 cm long.The inner diameter of a cross is 4cm.l, the outer diameter being 4.4 cm. find its
(i) Total surface area
Answers
A pipe will have two layers as shown in picture.
There is a inner Cylinder and Outer Cylinder.
Inner Radius = Inner Diameter / 2 = 4 / 2 = 2 cm = r
Outer Radius = Outer Diameter / 2 = 4.4/2 = 2.2 cm = R
Height of the pipe = 77 cm = h
Inner Surface area of the Pipe = 2∏rh = 2*22*2*77/7 = 968 Square cm.
Outer Surface area of the pipe = 2∏Rh = 2*22*2.2*77/7 = 1064.8 Square cm.
Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.
The cross section suface area is present at two ends of the pipe.
This is the area covered between 2 circles.
Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.
= 968 + 1064.8 + 2*∏(R^2 – r^2)
= 2032.8 + 2*22*(2.2*2.2 – 2*2)/7
= 2032.8 + 5.28
= 2038.08 Square cm.
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Answer:
R=2.2 cm, r=2 cm, h=77 cm
(i)S
1
=2πrh=2×
7
22
×2×77=968 cm
2
(ii)S
2
=2πRh=2×
7
22
×2.2×77=1064.8 cm
2
(iii)TSA=S
1
+S
2
+2(πR
2
−πr
2
)
=968+1064.8+2×
7
22
[(2.2)
2
−2
2
]=2028.08 cm