Respuesta :
Answer:
25:52 the ratio of the area of one of these spheres to the area of the original sphere.
Explanation:
Radius of metal sphere ,R= 9
Volume of metallic sphere, V = [tex]\frac{4}{3}\pi R^3[/tex]
Radius of small metal sphere = r
Volume of small sphere made form metal sphere = v
[tex]v=\frac{4}{3}\pi r^3[/tex]
Volume of metallic sphere = Total volume of all 3 small spheres
V = 3v
[tex]\frac{4}{3}\p R^3=3\times \frac{4}{3}\p r^3[/tex]
[tex]R=\sqrt[3]{3}r[/tex]
Area of sphere = [tex]4\pi (radius)^2[/tex]
Area of metal sphere = [tex]A=4\pi R^2[/tex]
Area of small metal sphere = [tex]A'=4\pi r^2[/tex]
The ratio of the area of small spheres to the area of the original sphere:
[tex]\frac{A'}{A}=\frac{4\pi r^2}{4\pi R^2}=\frac{r^2}{R^2}[/tex]
[tex]=\frac{r^2}{(\sqrt[3]{3}r)^2}=\frac{1}{(\sqrt[3]{3})^2}=\frac{1}{2.08}=\frac{25}{52}[/tex]
25:52 the ratio of the area of one of these spheres to the area of the original sphere.
