A metal pipe is 77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter being 4.4 cm
(see Fig. 13.11). Find its
(1) inner curved surface area,
(ii) outer curved surface area,
(ii) total surface area.
anyone please
Answers
ANSWER
(i) inner curved surface area
According to the question inner diameter is 4 cm,
then,
Inner radius of a cylindrical pipe =r
1
=
2
innnerdiameter
=(
2
4
)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
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
hope it helps u dear....
Answer:
(i) inner curved surface area
According to the question inner diameter is 4 cm,
then,
Inner radius of a cylindrical pipe =r 1 =innner diameter/2=( 4/2 )cm=2cm
Height (h) of cylindrical pipe=77 cm,
Curved Surface Area of inner surface of pipe =2πr1h
=(2×22/7 ×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 =outer diamterer/2
=( 4.4/2 )cm=2.2cm
Height of cylinder = h = 77 cm,
Curved area of outer surface of pipe = 2πr2 h
=(2× 22/7 ×2.2×77)cm ^2
=(2×22×2.2×11)cm ^2
=1064.8cm ^2
(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
=πr2^2 −πr1^2
= 22/7 ×((2.2) ^2 −(2) ^2 )
= 22/7 ×(4.84−4)
= 22/7 ×(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
hope it helps you mate ☺️