Question

B. 8/27 D. 1/3 10. Three spheres of radii , 2r, and 3r, respectively, are melted and formed into a new sphere. Find the surface area of this new sphere. A. 136.8 r(squared) C. 124.5 r(squared) B. 143.7 r(squared) D. 113.4 r(squared) 11. Three spheres of radii r, 2r, and 3r, respectively, are melted and formed into a new sphere. Find the volume of this new sphere. A. 54 pi r(cubed) C. 48 pi r(cubed) B. 43 pi r (cubed) D. 32 pi r(cubed)

Answer 1

`A_(f)=4\pi (\sqrt[3]{36} r)^(2)\\\\V_(f)=(4)/(3) \pi (36r^(3))`

Explanation:

In order to find the final radii of the sphere, we need to calculate the volume, knowing that volumes are additive:

`V_(1)=(4)/(3) \pi (r^(3))\\\\V_(2)=(4)/(3) \pi (2r)^(3)\\\\V_(3)=(4)/(3) \pi (3r)^(3)\\\\V_(f)=(4)/(3) \pi (r^(3)+(2r)^(3)+(3r)^(3))\\\\V_(f)=(4)/(3) \pi (r^(3)+8r^(3)+27r^(3))\\\\V_(f)=(4)/(3) \pi (36r^(3))\\\\V_(f)=(4)/(3) \pi R^(3)\\\\R=\sqrt[3]{36} r`

Now that we know the radii of the new sphere, we can calculate the surface area:

`A_(f)=4\pi R^(2)\\\\A_(f)=4\pi (\sqrt[3]{36} r)^(2)`