A metal pipe is 77cm long . The inner diameter of a cross section is 4 cm , the outer diameter being 4.4 cm . Find its
a) inner curved surface area
b) outer curved surface area
c) total surface area
Answers
Answer:
Inner Surface area of the Pipe = 968 Square cm.
Outer Surface area of the pipe = 1064.8 Square cm.
Total Surface Area = = 2038.08 Square cm.
Step-by-step explanation:
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.
Step-by-step explanation:
Given h = 77cm.
Given Inner Diameter of the cross-section d = 4cm.
Then the radius r = 4/2
= 2cm.
Given that Outer Diameter of the cross-section d = 4.4cm.
Then the radius R = 4.4/2
= 2.2cm.
(1) Inner curved surface area:
= 2pirh
= 2 * 22/7 * 2 * 77
= 2 * 22 * 11/7
= 968cm^2.
(2) Outer curved surface area:
= 2piRh
= 2 * 22/7 * 2.2 * 77
= 1064.8cm^2
(3) Total surface area:
= 2pirh + 2piRh + 2pi(R^2 - r^2)
= 968 + 1064.8 + 2 * 22/7((2.2)^2 - (2)^2)
= 968 + 1064.8 + 2 * 22/7(4.84 - 4)
= 2032.8 + 2 * 22/7(0.84)
= 2032.8 + 2 * 22 * 0.12
= 2032.8 + 5.28
= 2038.08cm^2.
Hope this helps!