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A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe. Find the diameter of the solid cylinder.

Answer:

**Solution:**

When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is.

Given inner diameter of the pipe = 6 cm

So inner radius, r = 6/2 = 3 cm

Outer diameter = 10 cm

Outer radius, R = 10/2 = 5 cm

Let h be the height of the pipe.

Volume of pipe =π (R^{2}-r^{2})h

= π (5^{2}-3^{2})×h

= π h(25-9)

= 16π h cm^{3}

Let r be the radius of solid cylinder.

Volume of solid cylinder = π r^{2}h

Since pipe is melted and changed into a cylinder, their volumes remains same.

π r^{2}h = 16π h

r^{2} = 16

r = 4 cm

Diameter = 2r = 2×4 = 8 cm

**Hence the diameter of the cylinder is 8 cm.**

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