Two metal spheres (one with radius x cm and the other with radius x+2 cm) will be melted together to create a new single sphere. Express the radius, R, of the new sphere as a function of x.

Question

whpalmer4 · Answer

Volume of a sphere is given by 
$$V = \frac{4}3\pi r^3$$So calculate the volume of both spheres.  Add the volumes together.  Now solve the volume equation for $r$ in terms of $V$, plug the combined volume into that equation as $V$ and find the value of $r$.

anonymous · Answer

so
$$4/3\pi x^3 +4/3\pi (x+2)^3=v$$
and then plug that in to solve for r?

whpalmer4 · Answer

Yeah.  You want to expand the left hand side first, though.  You'll find that the 4/3 pi stuff drops out as a common factor.

anonymous · Answer

$$(4/3\pi (x^3+(x+2)^3))/(4/3\pi)=r^3$$
$$\sqrt[3]{x^3+(x+2)^3}$$
does that simplify further to 2x+2 or does it stay as it is?