Question

A metal sphere of radius 9 is melted and transformed into three identical spheres. b What is the ratio of the area of one of these spheres to the area of the original sphere

Answer 1

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 = $\frac{4}{3}\pi R^3$

Radius of small metal sphere = r

Volume of small sphere made form metal sphere = v

$v=\frac{4}{3}\pi r^3$

Volume of metallic sphere = Total volume of all 3 small spheres

V = 3v

$\frac{4}{3}\p R^3=3\times \frac{4}{3}\p r^3$

$R=\sqrt[3]{3}r$

Area of sphere = $4\pi (radius)^2$

Area of metal sphere = $A=4\pi R^2$

Area of small metal sphere = $A'=4\pi r^2$

The ratio of the area of small spheres to the area of the original sphere:

$\frac{A'}{A}=\frac{4\pi r^2}{4\pi R^2}=\frac{r^2}{R^2}$

$=\frac{r^2}{(\sqrt[3]{3}r)^2}=\frac{1}{(\sqrt[3]{3})^2}=\frac{1}{2.08}=\frac{25}{52}$

25:52  the ratio of the area of one of these spheres to the area of the original sphere.