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A metallic pipe is 0.7 cm thick. Inner radius of the pipe is 3.5 cm and length is
5 dm. Find its total surface area.
fin (Hint: Total surface area. Inner surface area + Outer surface area + Area of two rims]
Answers
Step-by-step explanation:
(i) inner curved surface area
According to the question inner radius is 3.5 cm,
then,
Inner radius of a cylindrical pipe = r = 3.5
Height (h) of cylindrical pipe = h = 5dm
Height (h) of cylindrical pipe = 5/10= 0.5cm
Curved Surface Area of inner surface of pipe=2πrh
=2(22/7)(3.5)(0.5)
=(44/7)(1.75)cm
=(44/7)(1.75)cm
=11
(ii) Outer curved surface area
According to the question metallic pipe is 0.7 cm thick
Outer radius of cylindrical pipe = r =0.7cm
Height of cylinder = h = 0.5 cm,
Curved area of outer surface of pipe = 2πr^2h
=2(22/7)(0.7)^2(0.5)cm
=2(22/7)(0.49)(0.5)cm
=2(22/7)(0.245)
=(44/7)(0.245)
=1.534cm
(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 03.5 cm - Area of circle with radius 0.7 cm
= πr ^2 −πr^2
= (22/7)(3.5)^2 - (22/7)(0.7)^2
= (22/7) [(3.5)^2 - (0.7)^2]
= (22/7) [(12.25 - 0.49)]
= (22/7) [11.76]
= 37
Total surface area = curved surface area of inner cylinder + curved surface area of outer cylinder + 2 × Area of base
=11+1.534×37
= 67.758cm
Therefore, the total surface area of the cylindrical pipe is 67.758cm
Inner radius = r = 3.5 cm
External radius = R = r + h = 3.5 + 0.7 = 4.2 cm
Length = 5 dm = 50 cm
Total surface area of cylinder or pipe = 2∏(r + R) (h + R - r)
= 2 × 22/7 × (3.5 + 4.2) (50 + 4.2 - 3.5)
= 2453.88 cm2