Question

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form single sphere, the diameter of the sphere is

Answer 1

Answer:

The Diameter of the resulting sphere is 24 cm.

Step-by-step explanation:

Given:

Radius of first sphere (r1) = 6 cm

Radius of second sphere (r2) = 8 cm

Radius of third sphere (r3) = 10 cm

Let us assume the radius of the unknown sphere as = r

From the question we can say that:

$\large{\boxed{\boxed{\text{VolumeOfThreeSmallSphere=VolumeOfTheResultingSphere}}}}$

Formula to find the volume of Sphere:

$\huge{\boxed{\boxed{\red{\sf{4/3\pi r^{3}}}}}}$  

Solving the Question:

$4/3$$\pi$$r1^{3}$+$\pi$$r2^{3}$+$\pi$$r3^{3}$=$4/3$$\pi$$r^{3}$

Substituting the values of r in the equation:

$4/3$$6^{3}$$\pi$+$4/3$$8^{3}$$\pi$+$4/3$$10^{3}$ $\pi$= 4/3 $\pi$$r^{3}$

We take 4/3$\pi$common over here:

$4/3$$\pi$($6^{3}+8^{3}+10^{3}$) =$4/3$$\pi$$r^{3}$

4/3$\pi$ gets canceled:

$6^{3}$ + $8^{3}$ + $10^{3}$ = $r^{3}$

216 + 512 + 1000 = $r^{3}$

1728 = $r^{3}$

$r^{3}$ = $\sqrt[3]{1728}$

$r$ = $12 cm$

In the question we are asked to find the Diameter of the Sphere:

Diameter of the sphere = 2 * Radius

=> 2 * 12 = 24 cm

Therefore, the Diameter of the resulting sphere is 24 cm.