64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r. Option 1: 2 : 1 Option 2: 3 : 1 Option 3: 8 : 1 Option 4: 4 : 1

Answer: 4 : 1. Solution: 64 x (4/3) r^3 = (4/3) R^3. So R^3 = 64 r^3, giving R = 4r. Hence R : r = 4 : 1.

Geometry

Solids

Medium

64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.

2 : 1

3 : 1

8 : 1

4 : 1

✅ Correct Option: 4

$64 \times (4/3)\pi r^3 = (4/3)\pi R^3$ . So $R^3 = 64 r^3$ , giving $R = 4r$ . Hence $R : r = 4 : 1$ .

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64 solid iron spheres of radius r are melted to form a sphere of radius R. Find R : r.

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