Question

Metallic spheres of radii 6cm, 8cm and 10cm respectively are melted to form a

solid sphere. Find the radius of the resulting sphere.​

Answer 1

Answer:

the radius of the resulting sphere is 12cm

Step-by-step explanation:

the addition of the volume of the 3 spheres = volume of the resulting sphere

=> 4/3π(6)^3+ 4/3π(8)^3+ 4/3π(10)^3 = 4/3πr^3

=> 4/3π [ (6)^3 + (8)^3 + (10)^3] = 4/3πr^3

=> r^3= 216 + 512 + 1000

=> r^3 = 1728

=> r = 12cm

Answer 2

GIVEN:-

Radius (r1) of 1st sphere = 6cm

Radius (r2) of 2nd sphere = 8cm

Radius (r3) of 3rd sphere = 10cm

Radius of resulting sphere = r

$\therefore$ Volume of 3 spheres = Volume of resulting sphere

$\implies$$\small\sf{\frac{4}{3} \pi( {r1}^{3} + {r2}^{3} + {r3}^{3} ) = \frac{4}{3} {\pi \: r}^{3}}$

$\implies$$\small\sf{ \frac{4}{3} \pi( {6}^{3} + {8}^{3} + {10}^{3} ) = \frac{4}{3} {\pi \: r}^{3}}$

$\implies$$\small\sf{{r}^{3} = 216 + 512 + 1000}$

$\implies$$\small\sf{{r}^{3} = 1728}$

$\implies$$\small\sf{r = \sqrt[3]{1728}}$

$\implies$$\small\sf{r=12cm}$