Twenty-seven solid gold spherical beads each of radius 3 are melted down and recast into a larger, solid gold sphere. How many units are in the radius of this larger gold sphere

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.

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

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