Question

metallic spheres of radii 6cm.8cm and 10cm respectively are melted to form a single solid sphere

Answer 1

Volume conserved so on both side 4/3 pie will be cancelled

Answer 2

Appropriate Question:

Metallic Spheres of radii 6 cm , 8 cm and 10 cm respectively are melted to form a single sphere . find yhe rafius of the resulting sphere .

Solution :

Radii of given spheres are 6 cm , 8 cm and 10 cm .

$\sf{}Radius \: of \: Sphere_{(1)} = r_{(1)} \\ \\ \sf{}Radius \: of \: Sphere_{(2)} = r_{(2)} \\ \\ \sf{}Radius \: of \: Sphere_{(3)} = r_{(3)} \\ \\ \sf{}Radius \: of \: Sphere_{(4)} = r_{(4)}$

Now , volume of resulting sphere = sum of the volumes of given spheres.

$\sf{}r_{1} + r_{2} + r_{3} = r_{4}$

$\sf{} \dfrac{4}{3} \pi \: r_{(4)} ^{3} = \dfrac{4}{3} \pi \: r_{(1)} ^{3} + \dfrac{4}{3} \pi \: r_{(2)} ^{3} + \dfrac{4}{3} \pi \: r_{(3)} ^{3} \\ \\ \sf{}\sf{} \dfrac{4}{3} \pi \: r_{(4)} ^{3} = \dfrac{4}{3} \pi \: (6) ^{3} + \dfrac{4}{3} \pi \: (8) ^{3} + \dfrac{4}{3} \pi \: (10) ^{3} \\ \\ \sf{} r_{(4)} ^{3} = 216 + 512 + 1000 \\ \\ \sf{}r_{(4)} ^{3} = 1728 \\ \\ \sf{} \:r_{(4)} = 12 \: cm$

Therefore , radius of the resulting sphere is equals to 12 cm.

$\underline{ \underline{ \sf{ \red{ \bold{ more \: Formulas}}}}} \\ \\ \: \sf{}voume \: of \: cube \: = {a}^{3} \\ \\ \sf{}volume \: of \: cylinder = \pi {r}^{2} h \\ \\ \sf{}volume \: of \: cone = \frac{1}{3} \pi \: {r}^{2} h \\ \\ \sf{}volume \: of \: sphere \: = \frac{4}{3} \pi \: {r}^{3} \\ \\ \sf{} volume \: of \: hemisphere = \frac{2}{3} \pi {r}^{3}$