A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
A. 3.6 kg
B. 3.696 kg
C. 36 kg
D. 36
Answers
In order to find the weight of the pipe. .1st we need to find the volume of the solid region of the pipe and in order to find the volume of the solid region of the pipe. .1st we need to find the area of solid region of the pipe.
Area of the solid region of pipe = Total area of the circular cross section - hollow area of the circular cross section.
Total Area of cross section = πr² (where r is the external radius)
=π × 4 × 4 = 50.26 cm²
given the thickness of the solid section is 1 cm.
⇒ the radius of the hollow region = 4 - 1 = 3 cm.
Area of Hollow circular cross section = πr² ( where r is the hollow circular section radius)
= π × 3 × 3 = 28.27 cm²
⇒ Area of the solid region of pipe = (50.26 - 28.26) = 22 cm²
Volume of the solid region of pipe = Area of the solid region × length of the pipe
given the length of the pipe = 21 cm
⇒ Volume of the solid region of pipe = 22 cm² × 21 cm = 462 cm³
given that 1 cm³ weighs 8 grams
⇒ 462 cm³ weighs (462 × 8) grams = 3696 grams
we know that 1000 grams = 1 kg
⇒ 462 cm³ weighs 3.696 kg
⇒ The hollow iron pipe weighs 3.696 kg
Answer: Option B Explanation: In this type of question, we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow. Oh! line become a bit complicated, sorry for that, lets solve it. External radius = 4 cm Internal radius = 3 cm [because thickness of pipe is 1 cm] Volume of iron =πr2h=227∗[42−32]∗21cm3=227∗1∗21cm3=462cm3 Volume of iron =πr2h=227∗[42−32]∗21cm3=227∗1∗21cm3=462cm3 Weight of iron = 462*8 = 3696 gm = 3.696 kg