Question

if there are 3 gold spheres with a radius 3mm, 4mm, 5mm. If the spheres are melted to form a new sphere what is its radius now?

Answer 1

Add the volumes together and solve for the radius.

Since \[V=(4/3)(\pi)r ^{3}\]The sum of the volumes must equal
\[V _{1}+V _{2}+V _{3}=(4/3)(\pi)r_{t} ^{3}\]Solve for r and you get:
\[\sqrt[3]{(1/\pi)(3/4)(V _{1}+V _{2}+V _{3})}=r _{t}\]
Now just plug in the volumes into v1 v2 and v3 and you will achieve the final radius

Answer 2

My advice is to find the total volume of those 3 spheres added together. That will be the volume of the new sphere. Then you could work backwards to find the radius. The formula is: \[v=\frac{4}{3} \pi r^3\]

Answer 3

Solve the following equation for r inspired by Dalvoron:\[\frac{4}{3} \pi r^3=\sum _{r=3}^5 \frac{4}{3} \pi r^3 \]r = 6