Question

twenty seven solid iron spheres, each of radius r and surface area s are melted to form a sphere with surface area s. find the i) radius r of the new sphere ii) ratio of s and s

Answer 1

Answer:

Radius of the new sphere is 3 times the radius of the old spheres, i.e. 3r.

And ratio of the old surface area to the new surface area is 1:9.

Step-by-step explanation:

Since, volume of the new sphere is equal to the volume of all 27 spheres combined.

therefore we've :

$27 \frac{4}{3} \pi {r}^{3} = \frac{4}{3} \pi{(rn)}^{3} \\ = > rn = 3r$

where r and rn are radii of old and new spheres respectively.

Now for ratio of surface area of the old sphere to the new sphere we've:

$\frac{4\pi {r}^{2} }{4\pi {(rn)}^{2} } = \frac{4\pi {r}^{2} }{4\pi {(3r)}^{2} } = \frac{1}{9}$