Two metal spheres (one with radius x cm and the other with radius x+7 cm) will be melted together to create a new single sphere. Express the radius, R, of the new sphere as a function of x.

I got as far as figuring out the volumes would be added which equals:
(4pi(x)^3)/3 + (4pi(x+7)^3) = Volume of the new sphere. Not sure how to express the radius from that though. Thank you!

Question

Two metal spheres (one with radius x cm and the other with radius x+7 cm) will be melted together to create a new single sphere. Express the radius, R, of the new sphere as a function of x.

I got as far as figuring out the volumes would be added which equals:
(4pi(x)^3)/3 + (4pi(x+7)^3) = Volume of the new sphere. Not sure how to express the radius from that though. Thank you!

anonymous · Answer

(4pi(x)^3)/3 + (4pi(x+7)^3) = 4/3 *pi*R^3

anonymous · Answer

actually, a '3' is missing from your expression...  so:
4/3 * pi* (x^3 + (x+7)^3)  = 4/3 * pi* R^3

anonymous · Answer

simplify, etc.

anonymous · Answer

Thank you so much!