a man has three golden spheres with radius 1mm,2mm,3mm,respectively. He plans to melt it and make a larger sphere. What will be the radius of the larger sphere?

volume of 3 spheres

= (4/3)π( 1^3 + 2^3 + 3^3)
=(4/3)π(36)
= 48π

then for new sphere
(4/3)π r^3 = 48π
r^3 = 36
r = (36)^(1/3) = appr. 3.3

To find the radius of the larger sphere, we can use the concept of volume. The sum of the volumes of the smaller spheres should be equal to the volume of the larger sphere.

Let's denote the radius of the larger sphere as R. The formula for the volume of a sphere is given by V = (4/3) * π * r^3, where V represents the volume and r represents the radius.

Now, let's calculate the volumes of the smaller spheres:

Volume of the first sphere (r = 1mm): V₁ = (4/3) * π * (1mm)^3
Volume of the second sphere (r = 2mm): V₂ = (4/3) * π * (2mm)^3
Volume of the third sphere (r = 3mm): V₃ = (4/3) * π * (3mm)^3

To get the volume of the larger sphere, we need to sum up the volumes of the three smaller spheres:

Total volume of smaller spheres: V_total = V₁ + V₂ + V₃

Now, we can set V_total equal to the volume of the larger sphere and solve for its radius R:

(4/3) * π * R^3 = V_total

After rearranging the equation and solving for R, we can find the radius of the larger sphere.