17
A solid iron sphere of diameter 6 cm is melted and made into a hollow cylindrical pipe of external diameter 10 cm and of length 4 cm. The thickness of the pipe is:
- A1 cm
- B2 cm
- C4 cm
- D8 cm
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
The volumes of the sphere and of the pipe will be the same.
Diameter of sphere = 6 cm
∴ radius of sphere = 6/2 = 3 cm
Volume of the sphere = 4πr3/3 = 4π(3)3/3 = 36π
Let the internal radius of pipe be r.
Volume of the hollow cylindrical pipe = πh (R2 – r2) where h= height, R = external radius= 10/2 = 5 cm.
Hence,
36 π = π (4)(52 – r2)
⇒ 25 – r2 = 9
⇒ r2 = 16
⇒ r = 4 cm
⇒ Thickness = R – r = 5 – 4 = 1 cm
Diameter of sphere = 6 cm
∴ radius of sphere = 6/2 = 3 cm
Volume of the sphere = 4πr3/3 = 4π(3)3/3 = 36π
Let the internal radius of pipe be r.
Volume of the hollow cylindrical pipe = πh (R2 – r2) where h= height, R = external radius= 10/2 = 5 cm.
Hence,
36 π = π (4)(52 – r2)
⇒ 25 – r2 = 9
⇒ r2 = 16
⇒ r = 4 cm
⇒ Thickness = R – r = 5 – 4 = 1 cm