A hollow copper pipe is 22cm long and its external diameter is 28cm. If the thickness of the pipe is 3cm and iron weighs 8.5g/cm
3
, then the weight of the pipe is closest to:
- A34 kg
- B44 kg
- C14 kg
- D24 kg
Solution & Step-by-step Explanation
Given parameters:
Length (height, h) of the pipe = 22cm
External diameter = 28cm⟹External radius (R)=
2
28
=14cm
Thickness = 3cm⟹Internal radius (r)=R−thickness=14−3=11cm
Density = 8.5g/cm
3
The volume of material in a hollow cylinder is given by:
V=π(R
2
−r
2
)h
V=
7
22
×(14
2
−11
2
)×22
V=
7
22
×(196−121)×22
V=
7
22
×75×22
V=
7
36300
≈5185.71cm
3
Now, weight of the pipe:
Weight=Volume×Density
Weight=
7
36300
×8.5g
Weight=
7
308550
≈44078.57g
Converting to kilograms (kg):
Weight in kg=
1000
44078.57
≈44.08kg
The closest value among the options is 44kg.
Length (height, h) of the pipe = 22cm
External diameter = 28cm⟹External radius (R)=
2
28
=14cm
Thickness = 3cm⟹Internal radius (r)=R−thickness=14−3=11cm
Density = 8.5g/cm
3
The volume of material in a hollow cylinder is given by:
V=π(R
2
−r
2
)h
V=
7
22
×(14
2
−11
2
)×22
V=
7
22
×(196−121)×22
V=
7
22
×75×22
V=
7
36300
≈5185.71cm
3
Now, weight of the pipe:
Weight=Volume×Density
Weight=
7
36300
×8.5g
Weight=
7
308550
≈44078.57g
Converting to kilograms (kg):
Weight in kg=
1000
44078.57
≈44.08kg
The closest value among the options is 44kg.