1.

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:1). 1 cm2). 2 cm3). 4 cm4). 8 cm

Answer»

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


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