Answer:
[tex]243^{2/3}:324[/tex] or approximately 0.481
Step-by-step explanation:
Volume of a sphere: 4/3πr³
Surface area of a sphere: 4πr²
The initial sphere of radius 9 has a volume of [tex]\displaystyle\\9^3\cdot \frac{4}{3}\cdot \pi=972\pi[/tex]
When melted into three identical spheres, each must have a volume of [tex]\displaystyle \frac{972\pi}{3}=324\pi[/tex]
The radius of the smaller spheres must be:
[tex]\frac{4}{3}\pi r_s^3=324\pi \implies r_s=\sqrt[3]{243}\approx 6.24[/tex]
Surface area of each smaller sphere:
[tex]\displaystyle \\4\pi r^2\vert_{r=6.24}\approx 155.76\pi[/tex]
Surface area of initial sphere:
[tex]\displaystyle \\4\pi r^2\vert_{r=9}\approx 324\pi[/tex]
The desired ratio is [tex]155.76/324\approx \boxed{0.481}[/tex]
Exact: [tex]243^{2/3}:324[/tex]
