Question

Metallic spheres of radi 6 cm, 8 cm and 10 cm, respectively, are melted to form a
single solid sphere. Find the radius of the resulting sphere.​

Answer 1

Step-by-step explanation:

when we remake something

we should taken the formula of volume

hope u understand

Answer 2

Given:

Metallic spheres of radii 6 cm, 8 cm, and 10 cm.

According to the question:

The metallic spheres are melted to form a  single solid sphere.

To be found:

The radius of all three spheres.

• SOLUTION:

As they are melted to form a single sphere then the volume of single solid sphere will be equal to the sum of volumes of the three spheres.

Let, r₁, r₂, r₃ be the radii of the three spheres.

And let the radius of the big sphere be R.

So,

r₁ = 6cm

r₂ = 8cm

r₃ = 10cm

Now,

The volume of Sphere 1

(V₁) = 4/3 πr₁³

     = 4/3 π (6)³

     = 864/3 π cm³

• The volume of the sphere 2

(V₂) = 4/3 πr₂³

     = 4/3 π (8)³

     = 2048/3 π cm³

• The volume of the sphere 3

(V₃) = 4/3 πr₃³

     = 4/3 π (10)³

     = 4000/3 π cm³

Now,

According to the question,

The volume of three metallic spheres = Volume of a single solid sphere

⇒ V₁ + V₂ + V₃ = V(big sphere)

$\implies \frac{864}{3}\pi +\frac{2048}{3}\pi + \frac{4000}{3}\pi = \frac{4}{3} \pi R^{3}$

$\implies \frac{6912}{3} = \frac{4}{3} R^{3}$

$\implies R^{3} = \frac{6912}{\not3} \times \frac{\not3}{4}$

$\implies R^{3} = 1728$

$\implies R = \sqrt[3]{1728}$

$\implies \boxed{\bf{R = 12}}$

Hence,

The Radius of the big sphere is 12cm.