A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, 'the outer diameter being 4.4 cm
. Find its
c/ inner curved surface area,
outer curved surface area,
n
(in total surface area.
Answers
Answer:
inner curved surface area
According to the question inner diameter is 4 cm,
then,
Inner radius of a cylindrical pipe =2cm
Height (h) of cylindrical pipe=77 cm,
Curved Surface Area of inner surface of pipe =2πr = 968
(ii) Outer curved surface area
According to the question outer diameter is 4.4 cm
Outer radius of cylindrical pipe =2.2cm
Height of cylinder = h = 77 cm,
Curved area of outer surface of pipe = 2
=1064.8cm
(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
= 2.74
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
Therefore, the total surface area of the cylindrical pipe is
=2039.08cm
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!