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Explanation:
Let's calculate the volume of one small spherical bead
V = (4/3)*pi*r^3
V = (4/3)*pi*3^3
V = 36pi
The volume of 27 such identical beads is 27*36pi = 972pi cubic units.
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This is the new volume and we'll use this to find the radius r of the larger sphere.
V = (4/3)*pi*r^3
972pi = (4/3)*pi*r^3
3*972pi = 4pi*r^3
2916pi = 4pi*r^3
r^3 = (2916pi)/(4pi)
r^3 = 729
r = (729)^(1/3)
r = 9 units is the radius of the larger gold sphere
